All AP Physics C: Mechanics Resources
Example Question #1 : Circular Motion
A ball of mass is tied to a rope and moves along a horizontal circular path of radius as shown in the diagram (view from above). The maximum tension the rope can stand before breaking is given by . Which of the following represents the ball's linear velocity given that the rope does not break?
None of these
This is a centripetal force problem. In this case the tension on the rope is the centripetal force that keeps the ball moving on a circle.
If we want for the rope not to break, then the tension should never exceed .
Now we just solve for velocity: