# Centripetal Force Apparatus

Centripetal Force Apparatus

Equipment:

• Centripetal force apparatus

Demo:

A tennis ball is attached to a circular scale by a string. By holding the rod vertically and swinging the tennis ball in a circle, overhead, a centripetal force is produced and can be measured on the scale (in Newtons).

Explanation:

The force on the ball when it is moving in a uniform circular motion is the tension force $F_{T}$, which exerts force on the force meter. This occurs because the person exerts the same force on the string as the ball exerts on the string, indicated by the two red vectors in figure 1. Figure 1, below, is a top down view of the ball moving in a uniform circle. We can assume that the ball is moving in a completely horizontal frame.

Figure 1

If we apply Newton’s second law to the radial direction, which is horizontal, we get the following equation:
$F_{T}=m\frac{v^{2}}{r}$
Where m is the mass of the ball, v is the velocity and r is the radius of the uniform circle. $F_{T}$ is the force  due to tension and is the force we will read off of the scale on the apparatus.

Without this tension force, the ball would just fly off in a straight line tangential to its position on the uniform circle. In Figure 1, if the string was cut at that specific moment in time it would fly off in the direction of the velocity vector that is drawn on this free body diagram.

Written by: Nick McCabe