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Outline:

This is an introductory module in Classical Mechanics. ÌýStarting from Newton's Laws of Motion, it sets up the techniques used to apply the laws to the solution of physical problems. ÌýIt is essential background for many of the succeeding modules within the degrees in Physics and Astronomy. This module aims to allow students to understand the importance of classical mechanics in formulating and solving problems in many different areas of physics, develop problem-solving skills more generally, to introduce the basic concepts of classical mechanics and apply them to a variety of problems associated with the motion of single particles, interactions between particles and the motion of rigid bodies.Ìý

Aims:

This module aims to:
•ÌýÌý Ìýconvey the importance of classical mechanics in formulating and solving problems in many different areas of physics and develop problem-solving skills more generally;
•ÌýÌý Ìýintroduce the basic concepts of classical mechanics and apply them to a variety of problems associated with the motion of single particles, interactions between particles and the motion of rigid bodies.

Intended Learning Outcomes:

After completing this module students should be able to:

• state and apply Newton’s laws of motion for a point particle in one, two and three dimensions;
• use the conservation of kinetic plus potential energies to describe simple systems and evaluate the potential energy for a conservative force;
• understand an impulse and apply the principle of conservation of momentum to the motion of an isolated system of two or more point particles;
• evaluate kinematic quantities in the centre of mass system;
• solve for the motion of a particle in a one-dimensional harmonic oscillator potential with damping and understand the concept of resonance in a mechanical system;
• appreciate the distinction between inertial and non-inertial frames of reference, and use the concept of fictitious forces as a convenient means of solving problems in non-inertial frames;
• describe the motion of a particle relative to the surface of the rotating Earth through the use of the fictitious centrifugal and Coriolis forces;
• derive the conservation of angular momentum for an isolated particle and apply the rotational equations of motion for external torques;
• solve for the motion of a particle in a central force, in particular that of an inverse square law and so be able to describe planetary motion;
• describe the motion of rigid bodies, particularly when constrained to rotate about a fixed axis or when free to rotate about an axis through the centre of mass and and the motion of rolling objects with and without slipping;
• calculate the moments of inertia of simple rigid bodies and use the parallel and perpendicular axes theorems;
• appreciate the influence of external torques on a rotating rigid body.

Teaching and Learning Methodology:

This module is delivered via weekly lectures supplemented by a series of problem solving tutorials and additional discussion. In addition to timetabled lecture and PST hours it is expected that students engage in self-study in order to master the material. This can take the form, for example, of practicing example questions and further reading in textbooks and online.

Indicative Topics:

•ÌýÌý ÌýMathematical preliminaries. Units and dimensions, Vectors, Scalar and Vector Products, Calculus, Differentiation and Integration with vectors.
•ÌýÌý ÌýNewton's laws of motion. Symmetries, Invariance under spatial, time and rotational translations, boosts between frames of reference, motion under a constant force, momentum and impulse, projectile trajectories under gravity, conservation of momentum for isolated systems.
•ÌýÌý ÌýDefinitions of work, power, kinetic energy (KE) and potential energy (PE), conservative forces in one and three dimensions, friction and dissipative forces.
•ÌýÌý ÌýCentre of mass and collisions. Centre of mass, relative displacement and reduced mass, single-body collision with a rigid wall, coefficient of restitution, collision between two bodies of finite mass (head-on and glancing), inelastic vs elastic collisions.
•ÌýÌý ÌýPolar Coordinates, angular momentum, and motion in a central force. Motion in a plane expressed in plane polar coordinates, circular motion, angular momentum and torques, central forces, potential energy for a central force.
•ÌýÌý ÌýOrbits. Motion under inverse square law of force, Kepler's Laws, conic sections, eccentricity.
•ÌýÌý ÌýAccelerating and rotating frames of reference. Transformation of velocity and acceleration, rotating frames of reference, fictitious forces: centrifugal and Coriolis forces.
•ÌýÌý ÌýSimple Harmonic motion. Undamped motion, PE and KE in SHM, damped oscillations, forced damped oscillator.
•ÌýÌý ÌýRigid bodies. Angular momentum of a rotating rigid body, moment of inertia, KE of rotating body, equation of motion for a rotating body, compound pendulum, parallel and perpendicular axis theorem, centre of percussion, rolling vs slipping.