# Bowling ball sliding & rotating

1. Nov 19, 2014

### Samuelriesterer

Relative equations:
F_net = ma
a = F_net/m
f = N
= _net/I

Problem Statement:
A spherical bowling ball with mass m = 6.50 kg and radius R = 0.680 m is thrown down the lane with an initial speed of v = 9.00 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.12. Once the ball begins to roll without slipping it moves with a constant velocity down the lane.

Work done so far:
1) What is the magnitude of the angular acceleration of the bowling ball as it slides down the lane?

Isn’t this just zero because the ball is not rotating? I am confused about angular acceleration; is this the rate the angular velocity is changing, and angular velocity is the rate the angle is changing, that is rotating?

2) What is magnitude of the linear acceleration of the bowling ball as it slides down the lane?

F_net = -μN = -.12mg
a = F_net/m = .12g = -1.18 m/s^2

3) How long does it take the bowling ball to begin rolling without slipping?

v(t) = vi + at
ω(t) = αt
a = F_net/m
α = τ_net/I
I am told to find the t when v = rω but not sure about how to proceed.

4) How far does the bowling ball slide before it begins to roll without slipping?

5) What is the magnitude of the final velocity?

6) After the bowling ball begins to roll without slipping, compare the rotational and translational kinetic energy of the
bowling ball.

2. Nov 20, 2014

### haruspex

Just because it is sliding does not mean it is not rotating. When rolling, there is a relationship between the angular velocity and the linear velocity. That relationship does not suddenly become true from zero prior rotation. It takes time for the angular velocity to build to that level.
Draw a free body diagram for the sliding ball and derive equations for angular acceleration etc.