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 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 F_{spring}.
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 *m*_{2} 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 *m*_{1} 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
F_{spring} versus a_{c}.