ENGINEERING TRIPOS PART IB - 2012/2013
PAPER 1 - MECHANICS
Mechanics
Leader: Prof. D. Cebon
Timing: Weeks 1-8 Lent term
Structure: 16 lectures, 2 lectures/week
AIMS
The aims of the course are to:
- Show how the concepts of
kinematics are applied to rigid bodies.
- Explain how Newton's laws
of motion and the equations of energy and momentum are applied to rigid
bodies.
- Develop an appreciation of
the function, design and schematic representation of mechanical systems.
- Develop skills in modelling
and analysis of mechanical systems, including graphical, algebraic and
vector methods.
OBJECTIVES
As specific objectives, students should be able to:
Kinematics
- Specify the position,
velocity and acceleration of a rigid body in cartesian, polar and
intrinsic co-ordinates, using graphical, algebraic and vector methods.
- Understand the concepts of
relative velocity, relative acceleration and instantaneous centres of
rigid bodies.
Rigid Body Dynamics (mainly two-dimensional examples)
- Determine the centre of
mass and moment of inertia of a plane lamina.
- Understand and apply the
perpendicular and parallel axes theorems.
- Recognise whether a body is
in static or dynamic equilibrium.
- Understand the concepts of
energy, linear momentum and moment of momentum of a rigid body, and
recognise when they are conserved.
- 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.
- Determine the forces and
stresses in a rigid body caused by its motion.
- Understand simple
gyroscopic motion.
SYLLABUS (including book references)
Introduction and Terminology
1. Kinematics
- 1.1. Differentiation of
vectors (4: pp 490-492)
- 1.2. Motion of a particle Data
book p2
- 1.3. Motion of a rigid body
in space (3: ch 20)
- 1.4. Velocity and
acceleration images (1: p 124)
- 1.5. Acceleration of a
particle moving relative to a body in motion (2: pp 386-389)
2. Rigid Body Dynamics I - Inertia Forces and Energy
- 2.1. Centre of mass,
moments of inertia Data book Section 4
- 2.2. D'Alembert force for a
particle (3: p 101)
- 2.3. D'Alembert force and
torque for a rigid body in plane motion (4: pp 787-788)
- 2.4. Kinetic energy of a
rigid body in plane motion (2: p 461)
- 2.5. Conservation of energy
for conservative systems (3: pp 453-458)
- 2.6. Inertia forces in
plane mechanisms (1: pp 200-206)
- 2.7. Method of virtual
power (4: pp 429-432)
- 2.8. Inertia stress and
bending (1) Ch 5
- 2.9. Balancing simple
rotors (1: pp 180-182)
3. Rigid Body Dynamics II - Conservation of Momentum
- 3.1. Momentum of a rigid
body in plane motion (2: pp 267-271)
- 3.2. Moment of momentum
about G in plane motion (3: pp 555-558)
- 3.3. Moment of momentum
about a fixed point (4: p 894)
- 3.4. Impact problems in
plane motion (3: pp 487-493)
- 3.5. Introduction to
gyroscopic motion (2: pp 564-571)
- 3.6. Lamina rotating about an axis
in its own plane (1: pp 185-187)
REFERENCES
(1) BEER, F.P. & JOHNSTON, E.R. VECTOR MECHANICS FOR ENGINEERS: STATICS AND DYNAMICS
(2) HIBBELER, R.C. ENGINEERING MECHANICS – DYNAMICS (SI UNITS)
(3) MERIAM, J.L. & KRAIGE, L.G. ENGINEERING MECHANICS. VOL.2: DYNAMICS
(4) PRENTIS, J.M. ENGINEERING MECHANICS
Please see the Booklist for Part IB Courses for references for this module.
Last updated: May 2012
teaching-office@eng.cam.ac.uk
