Circular Motion

A particle is experiencing circular motion, as shown below.

Define the following variables:

R is the radius of the circle

w is the angular velocity in radians/s (at an instant)

α is the angular acceleration in radians/s² (at an instant)

v_T is the tangential velocity of the particle (at an instant)

a_T is the tangential acceleration of the particle (at an instant)

a_c is the (centripetal) acceleration of the particle towards the center of the circle (at an instant)

Now,

The above formulas tell us that (for the general case), when a particle is moving around a circular path, there is one component of velocity: tangential, and two components of acceleration: tangential and centripetal.

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