ROTATION OF RIGID BODIES
ANGULAR QUANTITIES
Angular displacement, 
where l is arc length and theta in radian
Angular velocity, ,ω = dθ / dt
Angular acceleration, α = Δω / Δt
Direction determine by right hand rule
Centripedal acceleration, aR = v² / R = (Rω)² / R = ω²R
Tangential acceleration, a tan = dv / dt = Rdω / dt = Rα
Frequency, f = ω / 2π = 1/ T
CONSTANT ANGULAR ACCELERATION
Torque
Lever arm
perpendicular distance from the axis of rotation to the line along
which the force acts.
Shorter lever arm , less torque used
Torque
Torque is the product of force and lever arm
T= R⊥F
ROTATIONAL DYNAMICS, TORQUE & ROTATIONAL INERTIA
Torque, T= mR^2a , ∑ T = (∑ mR2a)
Rotational inertia, l = ∑ miRi^2
The rotational inertia of an object depends not only on its mass distribution but also
the location of the axis of rotation
DETERMINING MOMENTS OF INERTIA
Moments of inertia, I =∫R^2dm
Parallex axis theorem
I = Icm + Mh^2
Perpendicular axis theorem (flat objects only)
Iz = Ix + Iy
ROTATIONAL KINATIC ENERGY
An object that is rotating has a rotational kinetic energy, rotational K =1/2Iw^2
If it’s translating as well, K = 1/2mv^2 + 1/2Iw^2
Work, W = TΔtheta
ROLLING
Rolling = rotational + translating
Why does a rolling sphere slow down?
No real sphere is perfectly rigid. The bottom will deform, and the normal force will
create a torque that slows the sphere