In rotational motion there are three types of accelerations to consider: centripetal, angular and tangential. What effect does a constant centripetal acceleration have on the other two
Centripetal acceleration is the one that keeps one object in a circular trajectory, changing the direction of the tangential velocity only.
The magnitude of the centripetal acceleration is proportional to the square of the tangential velocity, so, if the centripetal acceleration keeps constant, so does the tangential velocity.
Tangential acceleration, is just the rate of change of the tangential velocity, so, if the magnitude of the tangential velocity is the same at any point in the circle, tangential acceleration is just zero.
Angular acceleration is just the rate of change of the angular velocity.
Angular velocity, by definition, and the definition of angle, can be expressed as follows:
ω = v/R
where v is the tangential velocity, and R the radius of the circular trajectory.
So, if v keeps constant, ω keeps constant too.
Therefore, angular acceleration is also zero if the centripetal acceleration keeps constant.
As a conclusion, if the centripetal acceleration is constant, both tangential and angular acceleration are zero.
