Classical Mechanics: Kinematics and Dynamics

Study Notes

Classical mechanics is a branch of physics concerned with the motion of macroscopic objects, predicting how a body moves under forces.

Kinematics describes motion without considering its causes, focusing on displacement, velocity, and acceleration.
Displacement refers to the change in position of an object, and is a vector quantity.
Velocity is the rate of change of displacement, whether it is constant or instantaneous.
Acceleration is the rate of change of velocity.

Dynamics studies the causes of motion, linking force and mass to changes in motion.
Newton's laws of motion are fundamental:
- First law: An object remains at rest or in uniform motion unless acted upon by a force.
- Second law: Force equals mass times acceleration (F = ma).
- Third law: For every action, there is an equal and opposite reaction.
Force is an interaction that can change an object's motion.
Mass is the measure of an object's resistance to acceleration.
Weight is the force of gravity acting on an object (W = mg).
Momentum is the product of mass and velocity (p = mv).
Impulse is the change in momentum of an object.
Work is the energy transferred by a force acting over a distance (W = Fd cosθ).
Energy exists in various forms, including kinetic (energy of motion) and potential (stored energy).
The work-energy theorem states that the work done on an object equals its change in kinetic energy.
Power is the rate at which work is done (P = W/t).
Potential energy is energy possessed by an object due to its position or condition.
Conservation of energy states that in a closed system, the total energy remains constant.

Rotational motion describes the movement of an object around an axis.
Angular displacement is the angle through which an object rotates.
Angular velocity is the rate of change of angular displacement.
Angular acceleration is the rate of change of angular velocity.
Torque is the rotational equivalent of force (τ = rF sinθ).
Moment of inertia measures an object's resistance to rotational acceleration (I = Σmr²).
Angular momentum is the product of moment of inertia and angular velocity (L = Iω).
Conservation of angular momentum states that in a closed system, the total angular momentum remains constant.
Kinetic energy of rotation is given by KE = (1/2)Iω².

Simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement.
The period (T) is the time for one complete oscillation.
The frequency (f) is the number of oscillations per unit time (f = 1/T).
Amplitude is the maximum displacement from the equilibrium position.
Examples include a mass-spring system and a simple pendulum.

Wave motion involves the transfer of energy through a medium without the transfer of matter.
Transverse waves have oscillations perpendicular to the direction of wave propagation.
Longitudinal waves have oscillations parallel to the direction of wave propagation.
Wavelength (λ) is the distance between two successive crests or troughs.
Frequency (f) is the number of waves passing a point per unit time.
Wave speed (v) is the speed at which the wave travels (v = fλ).
Superposition is when waves overlap.
Interference can be constructive or destructive.
Diffraction is the bending of waves around obstacles.
The Doppler effect is the change in frequency of a wave due to the motion of the source or observer.

Fluid mechanics studies the behavior of fluids (liquids and gases).
Pressure is force per unit area (P = F/A).
Density is mass per unit volume (ρ = m/V).
Buoyancy is the upward force exerted by a fluid on an object.
Archimedes' principle states that the buoyant force equals the weight of the fluid displaced.
Fluid dynamics examines fluids in motion.
Viscosity measures a fluid's resistance to flow.
Surface tension is the force that causes the surface of a liquid to contract.