Motion Along A Circular Path

A body is rotating as shown below.

body rotating along a circular path

Define the following variables:

θ(t) is the angular rotation as a function of time

Δθ is the change in angle (angular displacement)

w is the angular velocity

α is the angular acceleration

t is time


equations for body rotating along a circular path

If we assume constant angular acceleration, we have the following formulas. Note that the subscripts 1 and 2 denote "initial" and "final".

equations for body rotating along a circular path 2

These formulas apply to every particle in a rigid body that is experiencing rotation, such as the disk shown in the first figure. In other words, all the particles experience the same angular displacement, angular velocity, and angular acceleration regardless of their position relative to the center of rotation.

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