Physics Formula Revision Rotational mechanics July - Dec 2008

Formula Sheet – rotational mechanics

Rotational kinematics

Angular variables

θ = angular position of the particle

ω = angular velocity = dθ/dt = lim∆t→0 ∆θ/∆t

α = angular acceleration = dω/dt = d²θ/dt²

If the angular acceleration is constant, formulas similar in form to linear formulas can be used to find the angular variables:

θ = ω₀t + ½ αt²

ω = ω₀ + αt

ω² = ω₀² + 2 α θ

where
ω₀ = angular velocity at the beginning

Relation between the linear motion of a particle of a rigid body and rotation of the rigid body

v = r ω
where
v = linear speed of the particle

a_t = rate of change of speed of the particle in circular motion

a_t = dv/dt = rdω/dt = r α (These relations are from the chapter of circular motion)