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 a_c, given by

where v is the speed of the rotating object, and r is the radius of the circle. The speed v of something moving in a circle at constant speed can be written as the circumference of the circle, divided  by the time it takes to go in the circle - or period T of the motion:

v = 2pr/T

so the acceleration can be written as

a_c = 4p²r/T².

So, by measuring T and r, you can determine the centripetal acceleration of the revolving object.

In this experiment, if the centripetal acceleration is produced by the force supplied by the hanging mass F_hang, then, according to Newton's Second Law

F_hang = m_stoppera_c 

where m_stopper is the mass of the revolving stopper.

We can verify this relationship by measuring the period of rotation and radius of circle for a number of different radii and then plotting T² vs r, which should have a linear relationship. It is an exercise for the lab student to do the last substitution and show what the slope of this graph should be. Note that the force supplied by the hanging mass is, because it is stationary, its weight:

F_hang = m_hangg.

Department of Physics