Engineering Tripos Part IA, 1P1: Mechanics, 2022-23
Course Leader
Lecturer
Lecturer
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
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
Lecturer
Lecturer
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
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
Lecturer
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
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
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
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
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
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
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
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
Register of non-UTO markers of Part II coursework
Last updated on 27/07/2023 09:50
Student records
Please ensure that you notify the Teaching Office immediately if you become aware of any student who withdraws or degrades from the course during the year. Please also let the Teaching Office know of any student who will not be returning to CUED next year e.g. changing course, or graduating after Part IIA. We do not always hear directly from Tutorial Offices.
Could you also inform us if there is a change in Director of Studies for your College.
Last updated on 27/07/2023 10:00
Engineering Tripos Part IIA, 3C7: Mechanics of Solids, 2024-25
Module Leader
Lecturers
Prof G Viggiani, Prof V.S. Deshpande
Lab Leader
Timing and Structure
Michaelmas Term, 16 lectures
Prerequisites
None
Aims
The aims of the course are to:
- Provide students with an understanding of how the stresses and strains within engineering components are related to both the loads and displacements imposed at their boundaries and to any thermal or inertial loadings to which they are subjected.
- Introduce analytical methods, predominantly for two-dimensional geometries, and for both elastic and plastic material responses.
- Illustrate the methods with a number of engineering case studies.
Objectives
As specific objectives, by the end of the course students should be able to:
- Calculate the stresses in an elastic or plastic axisymmetric system subjected to various loads.
- Use Airy and Prandtl stress functions to find analytical solutions to elastic problems.
- Apply upper- and lower-bound theorems to solid mechanics problems.
Content
Two-Dimensional Elasticity (6L): Prof. V.S. Deshpande
- Revision of stress and strain in 2D; Mohr's circle.
- Elastic constitutive relationship.
- Concepts of plane stress and plane strain.
- Equilibrium and compatibility equations in 2D; Cartesian and polar coordinates.
- Analysis of problems with circular symmetry: thick-walled tube, spinning disk, thermo-elastic problems.
Torsion, Stress Functions and Plasticity (4L): Prof. V.S. Deshpande
- Elastic torsion of prismatic bars: Prandtl stress function.
- Plastic torsion of prismatic bars.
- Airy stress function in Cartesian and polar coordinates.
- Stress distribution in an infinite plate with a circular hole or crack.
- Analysis of contact stresses; half-plane under line and distributed loads.
Stress analysis in 3D and Plasticity (6L): Prof F. Cirak
- Stress analysis in 3D: principal stresses; stress invariants; hydrostatic and deviatoric stresses; deviatoric stress invariants.
- Yield locus, pi-plane; symmetry; convexity; normality.
- Tresca and von Mises yield criteria; associated flow rules.
- Upper-Bound and Lower-Bound theorems.
- Applications of Upper-Bound and Lower-Bound theorems: thick-walled tubes; rotating disks.
- Revision of rigid block mechanisms: application to forming problems. Elasto-plastic analysis of a thick-walled tube.
Examples papers
There will be four Examples Papers, directly related to the lectures.
Coursework
Experimental Stress Analysis
Use experimental techniques to determine the stress concentration at the edge of a circular hole in finite plates.
Learning objectives:
- To develop an appreciation of errors that occur in experimental measurements of stresses using different experimental techniques.
- To learn about Digital Image Correlation.
- To note that the stress concentrations are sensitive to the location of the hole in the plate.
- To compare measured concentration factors with simple analytical predictions.
Practical information:
- Sessions will take place in the Structures Research Lab, Inglis Ground floor AND online.
- To sign-up go to http://www.eng.cam.ac.uk/teaching/apps/cuedle/index.php?context=3C7(bl377)
- Reports should be submitted online no later than 2 weeks after the lab session, before 4pm. There is an excel spreadsheet to submit too. Please, download from the same webpage.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA 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.
Last modified: 31/05/2024 07:28