Page 116 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 9

Circular Motion

and Gravitation

CENTRIPETAL ACCELERATION

A body that moves in a circular path at a velocity whose magnitude is constant is said to undergo uniform circular
motion.
Although the velocity of a body in uniform circular motion is constant in magnitude, its direction changes
continually. The body is therefore accelerated. The direction of this centripetal acceleration is toward the center
of the circle in which the body moves, and its magnitude is
v 2
a c =
r
(velocity of body) 2
Centripetal acceleration =
radius of circular path
Because the acceleration is perpendicular to the path followed by the body, its velocity changes only in direction,
not in magnitude.

CENTRIPETAL FORCE
The inward force that must be applied to keep a body moving in a circle is called centripetal force. Without
centripetal force, circular motion cannot occur. Since F = ma, the magnitude of the centripetal force on a body
in uniform motion is

mv 2
Centripetal force = F c =
r
SOLVED PROBLEM 9.1
A ball is whirled at the end of a string in a horizontal circle 60 cm in radius at the rate of 1 revolution
(rev) every 2 s. Find the ball’s centripetal acceleration.
The distance the ball travels per revolution is

s = 2πr = (2π)(0.6m) = 3.77 m
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