How does centripetal acceleration change as a mass is moved farther from the center of a rotating turntable?

Centripetal acceleration is defined as the acceleration directed toward the center of a circular path that an object moving in a circle must experience to maintain its circular motion. This acceleration can be calculated using the formula ( a_c = \frac{v^2}{r} ), where ( v ) is the tangential speed of the object, and ( r ) is the radius of the circular path.

As a mass is moved farther away from the center of the rotating turntable, the radius ( r ) increases. For an object moving in a circular path at a constant angular velocity, the tangential speed ( v ) is directly related to the radius by the equation ( v = \omega r ), where ( \omega ) is the angular velocity. As the radius increases, the tangential speed also increases because ( v ) becomes proportional to ( r ).

Since centripetal acceleration depends on the square of the tangential speed and the radius:

1. An increase in radius leads to a greater tangential velocity because ( v ) is increasing.

2. As a result, the centripetal acceleration increases since it is calculated based on the square of the tangential speed divided by the radius.

Thus