Undergraduate Teaching 2023-24

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Engineering Tripos Part IA, 1P1: Mechanical Vibrations, 2017-18

Lecturer

Prof R Langley

Timing and Structure

Weeks 7-8 Lent term and weeks 1-4 Easter term, 12 Lectures

Aims

The aims of the course are to:

  • Describe mathematically the behaviour of simple mechanical vibrating systems.
  • Determine the response of these systems to transient and harmonic excitation.
  • Analyse systems with more than one degree of freedom.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Obtain differential equations for mechanical systems comprising masses, rigid bodies, rotors, springs and viscous dashpots, noting the analogy with tuned electric circuits.
  • Reduce all differential equations to a standard form.
  • Solve these standard-form equations for the response to step, ramp, impulsive and harmonic excitation.
  • Understand the concept of damping and the meaning of damped natural frequency, damping factor and logarithmic decrement.
  • Obtain and solve differential equations in matrix form for mechanical systems with more than one degree of freedom.
  • Apply the rudimentary principles of modal analysis to the free vibration of a two-degree-of-freedom oscillator subject to initial conditions.
  • Apply these results to the design of a vibration absorber and to methods of vibration isolation.

Content

For each topic, the letter in parentheses is the link to the table at the bottom of the page, giving page numbers in the references.

Introductory material

  • The system elements: masses, rigid bodies, rotors, springs and dashpots and their analogies in tuned electric circuits: inductors, resistors and capacitors (a)
  • Obtaining differential equations for the motion of linear mechanical systems (b)

First order systems

Go to (c) for book reference pages (c)

  • Response to step, ramp and impulsive inputs (d)
  • Response to harmonic excitation (e)
  • Using the exp(iwt) notation for harmonic response calculations (f)

Second order systems

Go to (g) for book reference pages (g)

  • Response to step and impulsive inputs; free vibration and damped SHM (h)
  • Response to harmonic excitation (i)
  • Damping factor, logarithmic decrement, loss factor (j)

Systems with Two or more Degrees of Freedom

Go to (k) for book reference pages (k)

  • Degrees of freedom (l)
  • Equations of motion in matrix form, obtaining mass and stiffness matrices (m)
  • Natural frequencies and mode shapes (n)
  • Eigenvalues and Eigenvectors (o)
  • Free vibration and the superposition of modes (p)
  • Harmonic excitation (q)
  • Vibration isolation and absorption (r)

References

(1) DEN HARTOG, J.P. MECHANICAL VIBRATIONS
(2) HIBBELER, R.C. ENGINEERING MECHANICS: DYNAMICS (SI UNITS)
(3) MEIROVITCH, L. ELEMENTS OF VIBRATION ANALYSIS
(4) MERIAM, J.L. & KRAIGE, L.G. ENGINEERING MECHANICS. VOL.2: DYNAMICS
(5) PRENTIS, J.M. DYNAMICS OF MECHANICAL SYSTEMS

Relevant page numbers are given for each topic in the table. Parentheses indicate an incomplete treatment.

Topic Den Hartog Hibbeler Meirovitch Meriam & Kraige Prentis
a 2 (212) (57, 556) - 25, 27
b 10 212 537 543 25, 27
c 17 174 - - -
d 17 186 - - -
e 46 197 - - -
f 19, 47, 66 - - - 11
g 18 210 533 521 23
h 24 216 534 522 31, 37
i 50 219, 306 551 538 42, 47
j 24, 30, 53 (215) 540 (545) 38, 40
k 107 331 - - 79
l 107 331 - - 79
m 109, 145 - - - -
n 110 335 - - 79
o 161 - - - -
p 123 - - - 84
q 129 - - - 130
r 67, 131 313, 338 - - 69, 87

Booklists

Please see the Booklist for Part IA Courses for references to this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 31/05/2017 10:00

Engineering Tripos Part IA, 1P1: Mechanics, 2023-24

Course Leader

Dr T Butlin

Lecturer

Dr T Butlin

Lecturer

Dr J Talbot

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 30/05/2023 15:08

Engineering Tripos Part IA, 1P1: Mechanics, 2022-23

Course Leader

Dr T Butlin

Lecturer

Dr T Butlin

Lecturer

Dr J Talbot

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 27/09/2022 11:52

Engineering Tripos Part IA, 1P1: Mechanics, 2021-22

Course Leader

Prof H.E.M. Hunt

Lecturer

Prof H.E.M. Hunt

Lecturer

Dr J.P. talbot

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 11/10/2021 07:55

Engineering Tripos Part IA, 1P1: Mechanics, 2020-21

Course Leader

Dr T Butlin

Lecturer

Dr T Butlin

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 26/08/2020 09:15

Engineering Tripos Part IA, 1P1: Mechanics, 2019-20

Lecturer

Dr T Butlin

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please see the Booklist or Part IA Courses for references to this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 16/05/2019 08:16

Engineering Tripos Part IA, 1P1: Mechanics, 2018-19

Lecturer

Dr T Butlin

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
  • Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Instantaneous centres for planar motion [KRB4]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please see the Booklist or Part IA Courses for references to this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 18/09/2018 09:57

Engineering Tripos Part IA, 1P1: Mechanics, 2017-18

Lecturer

Dr T Butlin

Timing and Structure

Weeks 1-8, Michaelmas term, 2 lectures/week

Aims

The aims of the course are to:

  • Convey the fundamental role of mechanics in engineering.
  • Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
  • Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
  • Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
  • Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Apply concepts of kinematics to particles and rigid bodies in two dimensions.
  • Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
  • Differentiate a rotating vector.
  • Understand and apply Newton's laws and the equations of energy and momentum of particles.
  • Apply Newton's laws to variable mass problems.
  • Apply the concept of angular momentum of a particle, and recognise when it is conserved.
  • Apply the principles of particle dynamics to satellite motion.
  • Determine the centre of mass and moment of inertia of a plane lamina
  • Understand and apply the perpendicular and parallel axes theorems
  • Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
  • Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
  • Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
  • Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples, including impact in planar motion

Content

The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.

Introduction

  • Newton's laws of motion [I1]
  • Units [I2]
  • Forces [I3]
  • Free Body Diagrams [I4]
  • Frames of reference [I5]

Kinematics of Particles

  • Cartesian coordinates [KP1]
  • Polar coordinates [KP2]
  • Intrinsic coordinates [KP3]
  • Differentiation of a unit vector [KP4]
  • Velocity and acceleration in different coordinate systems [KP5]
  • Numerical differentiation [KP6]
  • Relative position, velocity and acceleration [KP7]

Dynamics of Particles

  • Newton's Laws applied to particles [DP1]
  • D'Alembert force for a particle [DP2]
  • Equations of motion [DP3]
  • Numerical solution methods [DP4]
  • Conservation of Energy [DP5]
  • Potential energy, equilibrium and stability [DP6]
  • Linear momentum [DP7]
  • Variable mass systems [DP8]
  • Angular momentum [DP9]
  • Satellite motion in steady circular and elliptical orbits [DP10]

Kinematics of Rigid Bodies

  • Relative motion [KRB1]
  • Angular velocity as a vector [KRB2]
  • Rotating reference frames [KRB3]
  • Velocity diagrams for planar motion [KRB4]
  • Velocity image and instantaneous centres for planar motion [KRB5]

Dynamics of Rigid Bodies

  • Centre of mass of a rigid body [DRB1]
  • Moment of inertia of a planar rigid body [DRB2]
  • Dynamics of a rigid body with a fixed axis of rotation [DRB3]
  • D'Alembert forces and moments for planar motion of a rigid body [DRB4]
  • Linear and angular momentum of rigid bodies in planar motion [DRB5]
  • Kinetic energy of a translating and rotating planar body [DRB6]
  • Impact problems in plane motion [DRB7]

REFERENCES

[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
​[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
 

Comments:

Gregory [1] is a rigorous textbook with a physics perspective.

Malthe-Sorrensson [2] has many numerical examples.

Hibbeler [3] contains many illustrative diagrams and examples.

Meriam and Kraige [4] contains many illustrative diagrams and examples.

Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.

Topic cross references

Topic codes with textbook section numbers (incomplete treatment denoted by parentheses)
  Gregory Malthe-Sorrenssen Hibbeler Meriam Kraige Prentis
I1 3.1 5.3, 5.8, 5.9 1.2, 13.1 1.3  
I2 3.1 3.1, 3.2 1.3, 13.1 1.4  
I3 3.3 5.4 - 5.7 1.2    
I4   5.2, 7.1 3.2 3.3  
I5 3.2 5.8, 6.4 13.2 1.2  
KP1 (1.1 - 1.2) 6.2 2.5 - 2.7 2.4  
KP2 2.3   12.8 2.6  
KP3     12.7 2.5  
KP4 2.3     2.6, 5.7  
KP5 (2.3)   12.4, 12.5, 12.7 2.4 - 2.6  
KP6   4.1 - 4.2      
KP7 (2.6)   12.10 2.8  
DP1 4.1 - 4.5 5.3, 7.2 - 7.6 13.1 - 13.2 3.1 - 3.5, 4.2  
DP2 12.4   13.2 (3.14)  
DP3 4.1-4.5 (7.2 - 7.6) 13.2 - 13.6 3.4 - 3.5  
DP4   4.2, 7.4, 7.5, 7.6, 10.3   (C.12)  
DP5 6.1,6.2, 6.4 (11.1, 11.2) 14.1 - 14.2, 14.5 - 14.6 3.6 - 3.7  
DP6 6.3 11.3   (3.7)  
DP7 10.1 - 10.4 12.2 - 12.6 15.1 - 15.4 3.8 - 3.9  
DP8 (10.5) 12.7 15.9 4.7  
DP9 11.1 - 11.2 16.4 15.5 - 15.7 3.10 5.6
DP10 7.1, 7.2, 7.3, 7.5, 7.6 (5.5, 7.6) 13.7 3.13  
KRB1 2.6   16.7 - 16.8 (3.14), 5.4, 5.6 4.3, 4.8
KRB2 16.1 14.6 16.3, 20.1 5.2, 7.3 4.4
KRB3 17.1   20.4 5.7 4.3
KRB4         4.4
KRB5     16.6 5.5 4.4, 4.7
DRB1 3.5, A.1 13.2 9.2, 13.3    
DRB2 9.4, A.2, A.3 15.2 17.1 7.7, B.1  
DRB3 11.6, 16.1 15.1 17.4 6.4  
DRB4 (11.6)   (17.2 - 17.5) 6.1 - 6.5 5.3
DRB5 11.4, 11.5, 11.6 15.1 19.1 - 19.4 6.8 5.6, 5.8
DRB6 9.4 15.2, 15.4, 15.5 18.1 - 18.5 6.6  
DRB7 10.6   19.2 - 19.4 6.8  

 

Booklists

Please see the Booklist or Part IA Courses for references to this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 08/08/2017 13:53

Transfers to MET from Chemical Engineering

Applications to MET are welcomed from second-year students studying Chemical Engineering. Such students do not require Faculty Board permission to enter MET Part IIA.  MET or IB Directors of Studies are requested to inform the MET office of any such applicants.  It would be helpful if the applicants' email addresses and the name and e-mail of their present Director of Studies could be given.

Last updated on 27/07/2023 09:59

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