Ferris Wheel Physics Problem?

Question

An object is being swung in a circular path at the end of a 30 meter cable. The ball
completes 120 revolutions each minute (120 RPM). What is the centripetal acceleration (in
m/s^2) of the object?

Answer 1

Mitchell,

 

We start with F = ma and then define centripetal force as F = mv²/r

 

setting the two expressions equal give:  ma = mv²/r

 

Since mass appears on both sides of this relation we can cancel mass out and get:

 

a = v²/r

 

So v²/r = centripetal acceleration.

 

All we need to do now is convert our angular speed in revolution per minute to meters per second.

 

120 rev/min x 2pi*r m/rev x 1 min/60 sec gives: (with r = 30 m)

 

120*2pi*30m/60 sec = 120*pi m/s

 

So v = 120*pi m/s

 

Square v and divide by r and you have your answer!