Centripetal Acceleration

Purpose:
To demonstrate that centripetal force, tangential velocity and radius are all related.

Equipment:
Tennis ball with string through PVC pipe Four hanging weights

Equipment Location:
Other

Procedure:
First place one hanging weight in the loop. Swing the ball around until the tape reaches the bottom of the PVC pipe. Next add the three other weights and again spin the tennis ball until the tape reaches the bottom of the PVC pipe. The speed of the ball should be noticeably greater this time. After that last demo you should pull on the sting so that the tennis ball starts coming closer to the PVC pipe. The tennis ball's speed should increase even more as it gets closer to the pipe.

Hints:
Whenever you are swinging the ball be very careful when you try to stop or you may end up hitting yourself with the ball as has happened to me many times in trying this demo. Also make sure that there is ample room so that you do not knock anything other objects over.

Relevant derivations/explanations:
The follow formula shows the relationships between different forces in the demonstration. Fc = Mwg = mbac = mbv2t/r The formula shows that the centripetal force is equal to the mass of the weights times gravity. That in turn is equal to the mass of the tennis ball times the centripetal acceleration which is also equal to the mass of the ball times the tangential velocity squared over the radius from the PVC pipe to the ball.