Rotational Motion
Angular Quantities
Arc length,s=rθ where r=radius of the circle,θ=angle(in radians)
Angular displacement = θ2-θ1 
VELOCITY
Angular velocity=rate of change of angular displacement with time. ω=θ/t 
Instantaneous angular
velocity=dθ /dt 
ACCELERATION
Angular acceleration(α)=rate of change of angular velocity with time 
Instantaneous angular acceleration=dω/dt 
Correspondence between linear
and angular quantities
s=rθ
v=rω
a=rα
Period(T)=time taken by the object to describe a circle. Unit=s
ω=θ/t=2π/T
T=2π/ω
Frequency(f)=number of complete circles moved by the object in a unit time. Unit=Hz
f=1/T=ω/2π or ω=2πf
Vector Nature of Angular Quantities
Direction of angular velocity can be determined by using RIGHT HAND GRID RULE.
Constant Angular Acceleration
TORQUE=product of force and lever arm. 
Axis of rotation: The point where the object rotates.
Lever arm: Perpendicular distance from the axis of rotation to the line along which the force acts.
Rotational Dynamics
Torque
Rotational Inertia(moment of inertia)
F=ma, a=rα
F=mrα
F(r)=mrα(r)
Fr=mr^2α
Depends on distribution of mass, shape and axis of rotation.
Determining Moments of Inertia
Parallel-axis theorem:If the moment of inertia about an axis passing through the center of mass, then the moment of inertia about a parallel axis displaced by a distance h from the center of mass axis is 
Perpendicular-axis theorem:The moment of inertia of a plane object about an axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane. 
Rotational Kinetic Energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy. 
Conservation of Energy 
Work done due to torque 
Rotational +Translational Motion = Rolling 
Why Does a Rolling Sphere Slow
Down?
- No real sphere is perfectly rigid
- The bottom will deform,
- The normal force
will create a torque that slows the sphere.
