Question

A tennis ball connected to a string fixed to a frictionless table travels in a horizontal circle at constant radius with decreasing angular velocity. If the string breaks, which describes the tennis ball's linear velocity right afterwards?

A. It is changing direction, but not magnitude.

B. It is constant.

C. It is changing magnitude, but not direction.

D. It is changing both magnitude and direction.

Answer 1

As the string breaks, the tennis ball will go tangential to the circle of revolution at the point where the string breaks.

Now it will have a horizontal component of velocity,let's say V_x. But now gravity will also act. And gravity will produce extra vertical component of velocity V_y . Thus the total velocity of the tennis ball will be the vector sum of V_x and V_y . And this total velocity will not be horizontal any more. The path will be parabolic, as it is one of the case of Projectile Motion.

So, the correct answer will be D. Because initial magnitude was just V_x and new magnitude is (V_x² + V_y² )^1/2 . And direction is changing too.