This calculus-based course is designed for students majoring in the Physical Science programmes. It is centered on the Newton’s laws and deals with the motion or the change in motion of physical objects with speeds much less than that of light (<<c). It considers kinematics, dynamics and statics. Other topics include central forces, planetary motion, work, energy and momentum of particles.
The detailed breakdown of the above topics are as follow:
Scalars and vectors, vector algebra, Laws of vector algebra, Unit vectors, Components of a vector, Dot or scalar product, Cross or vector product, Triple products, Derivatives of vectors. Integrals of vectors, Velocity, Acceleration. Relative velocity and acceleration, Tangential and normal acceleration. Notation for time derivatives, Gradient, divergence and curl, Line integrals.
Newton’s laws, Definition of force and mass, inertial frames of reference. Absolute motion, Work, Power, Kinetic energy, Conservative force fields, Potential energy or potentials, Conservation of energy, Impulse, torque and angular momentum, Conservation of momentum, Conservation of angular momentum, Non-conservative forces
Uniform force fields, uniformly accelerated motion. Weight and acceleration due to gravity, freely falling bodies. Projectiles, Potential and potential energy in a uniform force field, Motion in a resisting medium, constrained motion. Friction, statics in uniform gravitational fields
Central forces, some important properties of central force fields, Equations of motion for a particle in a central force field, important equations deduced from the equations of motion. Potential energy of a particle in a central force field, Conservation of energy, Determination of the orbit from the central force. Determination of central force from the orbit.