circular path of radius 2 m. Find the magnitude of the object’s
acceleration and the net force responsible for its motion.Here’s How to Crack It
By definition, an object moving at constant speed in a circular path is undergoing
uniform circular motion. Therefore, it experiences a centripetal acceleration of
magnitude v^2 /r, which is always directed toward the center of the circle.
Newton’s second law, coupled with the equation for centripetal acceleration, gives:
What is the
Centripetal Force?
The centripetal force is not
a new force that makes
things move in circles.
Rather, real forces (e.g.
gravity, friction, tension,
the normal) provide
the centripetal force
necessary to maintain
circular motion.This equation gives the magnitude of the force. As for its direction, remember that
because F = ma, the directions of F and a are always the same. Since centripetal
acceleration points toward the center of the circular path, so does the force that
produces it. Therefore, it’s called centripetal force. The centripetal force acting
on this object has a magnitude of Fc = mac = (5 kg)(18 m/s^2 ) = 90 N.
- A 10 kg mass is attached to a string that has a breaking strength
of 1,500 N. If the mass is whirled in a horizontal circle of radius 90
cm, what is the maximum speed it can have? (Neglect the effects of
gravity.)