Question

How much time passes before the bowling ball begins rolling without slipping?

a. The information is insufficient.
b. Time does not affect the ball's motion.
c. It depends on the ball's mass.
d. It depends on the initial conditions.

Answer 1

Therefore, the answer is d. The time it takes for a bowling ball to begin rolling without slipping depends on the ball's moment of inertia, which in turn depends on its mass distribution.

Step-by-step explanation:

To determine the time it takes for the bowling ball to begin rolling without slipping, we need to consider the forces acting on the ball. Since the ball starts rotating counterclockwise and there is friction between the ball and the lane, the force of friction acts in the opposite direction. The ball will begin rolling without slipping when the frictional force is equal to the torque due to the ball's rotation.

We can use the equation −kRF = Iɛ. R, where k is the coefficient of kinetic friction, R is the radius of the ball, F is the normal force, I is the moment of inertia, and ɛ is the angular acceleration. Since the ball is moving to the left, the frictional force points to the right and we can take it as positive.

By solving for ɛ, we find that ɛ = kRF / I. Since both k and R are constant for a given ball, the time required for the ball to start rolling without slipping depends on the ball's moment of inertia, which in turn depends on its mass distribution.