## Study

### Mechanics for Biomedical Engineering

Module Code:               4CCYB062

Credit:                            15
Module Organisers:     Dr Jordi Alastruey

Aims

This module will provide students with a fundamental knowledge of classical mechanics, including forces, Newton’s Law, conservation of energy and momentum, single particle & rigid body dynamics, central forces and oscillations. The student will learn how to solve problems in mechanics, for example through drawing force diagrams and resolving forces, and then applying Newton’s Laws and conservation laws.

Learning Outcomes

On completion of the course, the students should be able to:

• To demonstrate an understanding of the theoretical basis underlying the classical laws of Newtonian mechanics, such as Newton’s Laws and the conservation laws.
• To identify the most appropriate laws to apply to complex problems in mechanics, aided by the use of annotated diagrams.
• To apply the relevant laws and equations to solve complex problems in mechanics.
• To demonstrate a physical understanding and interpretation of the resulting solutions to such problems.

Teaching Methods

Lectures: 20
Tutorials: 20

Syllabus

Introduction to Mechanics:

• basic principles
• forces & vectors
• drawing diagrams
• units
• problem solving

Kinematics & Dynamics in 1D:

• displacement, time, velocity, acceleration
• instantaneous/ average velocity & acceleration
• motion with constant acceleration
• freely falling bodies
• velocity & position by integration

Kinematics & Dynamics in 2 & 3D:

• position, velocity & acceleration vectors
• projectile motion
• motion in a circle
• relative velocity

Newton’s Laws of Motion:

• force & interactions
• Newton’s 1st Law
• Newton’s 2nd Law
• mass & Weight
• Newton’s 3rd Law
• free-body diagrams

Applications of Newton’s Laws:

• particles in equilibrium
• dynamics of particles
• frictional forces
• dynamics of circular motion

Work & Kinetic Energy:

• work
• kinetic energy and the work-energy theorem
• work & energy with varying forces
• power

Potential Energy & Energy Conservation:

• gravitational potential energy
• elastic potential energy
• conservative & non-conservative forces
• force & potential energy

Momentum, Impulse & Collisions:

• momentum & impulse
• conservation of momentum
• collisions
• centre of mass

Rotation of Rigid Bodies:

• angular velocity & acceleration
• energy of rotational motion
• parallel-axis theorem
• moment of inertia

Dynamics of Rotational Motion:

• torque
• angular momentum & conservation
• work & power in rotational motion
• gyroscopes & precession

Equilibrium:

• conditions for equilibrium
• centre of gravity
• solving rigid-body problems

Gravitation:

• Newton’s Laws of gravitation
• weight
• gravitational potential energy
• orbits

Periodic Motion:

• 2nd order ODEs and their solution
• simple harmonic motion
• simple pendulum
• damped oscillations
• forced oscillations & resonance

Assessments

Type Weighting
Exam (2 hours) (May/June)  70%
Coursework (3 assessed courseworks)  30%