PHY 253 — CLASSICAL MECHANICS I

BSc BSc Physics · Kwame Nkrumah University of Science and Technology

Newton’s laws of motion ; equation of motion. Superposition of forces. Solution of the equation of motion for different forces. Dynamics of uniform circular motion. Centripetal force. Law of conservation of linear momentum. Centre of mass (CM), computation of CM’s of solid bodies. Motion of the CM. Energy of a system of particles. Motion of a rocket. Impulsive forces. Collisions in one and two dimensions. The ballistic pendulum. Collisions and reactions of nuclei and of elementary particles. Motion of a rigid body. Rotation about a fixed axis. Angular velocity and angular acceleration. Motion with constant angular acceleration. Kinetic energy of rotation; moment of inertia. Computation of moments of inertia of simple solid bodies. The inertia tenor. Angular momentum of a particle and of a rigid body. The torque; equation of rotational motion; conservation of angular momentum and its applications. Work, Energy and Power in rotational motion. Rolling motion. Precession of a Gyroscope. Classification of constraints: examples. Generalised coordinates. Conservative systems. The one-dimensional calculus of variations. Problems with fixed end points and its solution: the Euler-LaGrange equations. Solution of the Brachistochrone problem and other extremum problems. Hamilton’s principle. Derivative of the LaGrange equations of motion from the Hamilton principle. Application to simple mechanical systems executing small oscillations and to current oscillations in coupled electrical circuits.

Credits

2

Level

Level 200

Course details from Courses for BSc. Physics - Physics.