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 = ω

_{0}t + ½ αt²

ω = ω

_{0}+ αt

ω² = ω

_{0}² + 2 α θ

where

ω

_{0}= 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)

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