Question

A bowling ball with a radius of 12 cm is given a backspin (i.e. if you picture the ball moving to the right it is spinning counterclockwise at the same time) of 8.3 rad/ s and a forward velocity of 8.5 m/s.As a result, the ball slides along the floor. What is the forward velocity of the point on the ball that is touching the floor?
answer i 9.5 m/s but how?

Answer 1

We can solve this problem by adding the forward linear velocity of the ball to the linear velocity due to the rotation of the ball.

First, we need to find the linear velocity due to the rotation of the ball. We know the angular velocity (8.3 rad/s) and the radius of the ball (12 cm, or 0.12 m).

The linear velocity v due to rotation can be found by the formula:

v = r * ω

where r is the radius of the ball and ω is the angular velocity.

v = 0.12 m * 8.3 rad/s = 0.996 m/s

Now, we add the forward linear velocity (8.5 m/s) and the linear velocity due to rotation (0.996 m/s).

Forward velocity of the point touching the floor = 8.5 m/s + 0.996 m/s ≈ 9.5 m/s