## II. Theory

In order to cause a body to move in a circular path at constant speed, the resultant of all forces acting on that body must be directed toward the center of the circle. This resultant inward force is called the centripetal force. This centripetal force produces an inward radial acceleration, the centripetal acceleration ac, given by

where v is the tangential speed of the revolving object (C), and r is the radius of the circle. The tangential speed v, in m/s, is related to the angular speed, w, by

.

The angular speed, in rad/s, is given by

where T is the time for one revolution and f is the number of revolutions per second.

Combining the above three equations gives:

.

So, by measuring v and r --- or f and r --- you can determine the centripetal acceleration of the revolving object.

When (C) is revolving, the spring (G) supplies an inward force Fspring. We will measure this force by determining how much mass must be hung over the pulley (E) to stretch the spring and displace the stationary mass (C) to the same radial position as when it is rotating. The force supplied by the spring is then given by

where m2 is the mass hanging over the pulley.

If the centripetal acceleration is produced by the force supplied by the spring, then, according to Newton's Second Law

where m1 is the mass of the revolving object (C). We can verify this by comparing the measured mass of the object to the slope of the graph of Fspring versus ac.