Circular Motion, Gravitation, SHM

Angular Displacement

the angle in which a body has moved

Radians

angle subtended at the centre of the circle that has a arc in equal length to the radius

Angular Velocity

rate of change of angular displacement

Angular Acceleration

rate of change of angular velocity

Centripetal Force

resultant force acting on an object moving in a circle always directed to the centre of the circle

Newton's Law of Gravitation

The gravitational force is proportional to the product of 2 point masses and is inversly proportional to the square of their seperation. F = Gmm/r^2

Gravitational field strength, g

Gravitational force per unit mass on a point mass, g = F/m

Gravitational Field

Region of space where a force acts on a mass

Gravitational potential

Work done per unit mass in bringing a mass from infinity to that point in a gravitational field. -GM/r

negative because: Gravitational potential at infinity is 0, and gravitional force is attractive, so work done has to be done against to gain potential energy.

Geostationary Orbits

Circular orbit above the equator where a satellite has the same spinning period of the earth,

Gravitational Potential Energy

Energy of an object has because of its position in a grav field. -GMm/r

Amplitude

Maximum displacement from equilibrium position

Period

Time taken for one full/complete cycle

Simple Harmonic Motion

Acceleration is proportional to the displacement and is always directed towards equilibrium position. Acceleration and displacement are in opposite directions.

Damping

Reduction of amplitude of oscillations due to energy losses from the system due to resistive forces.

Under/Light damping

System keeps oscillating but at a smaller amplitude each time

Critical Damping

System returns to equilibrium in the shortest amount of time possible without oscillations

Heavy Damping

System returns to equilibrium at a very slow speed without any oscillations happening

Resonance

Resonance is when a system's amplitude increases greatly because the driving frequency matches its natural frequency

Forced oscillations

System is made to oscillate by applying a periodic external force, regardless of its natural frequency

Natural Frequency

A frequency at which a system oscillates on its own, without any external force