Bowling Ball Question 1: Solving for Skidding Time and Distance

[j126]

1. The Problem Statement
A bowler throws a bowling ball of radius R = 11 cm down the lane with initial speed v0 = 10.5 m/s. The ball is thrown in such a way that it skids for a certain distance before it starts to roll. It is not rotating at all when it first hits the lane, its motion being pure translation. The coefficient of kinetic friction between the ball and the lane is 0.32.

(a) For what length of time does the ball skid? (Hint: As the ball skids, its speed v decreases and its angular speed ω increases; skidding ceases when v = Rω.)

(b) How far down the lane does it skid?

(c) How fast is it moving when it starts to roll?

Homework Equations

kinematics equations and rotational motion equations; the only friction equation that I know is F_friction=(coefficient of friction)(F_normal)

The Attempt at a Solution

(a) I set up the equation: v_o+at=v_final=(initial rotational velocity)+(rotational acceleration)(time)
Then plugged in the only values I know: 10.5m/s-at=v_final=(rotational acceleration)(time)

This is where I got stuck, so I didn't begin parts (b) or (c).

 

[ehild]

The ball moves along a horizontal straight line. Its motion consists of a pure translation of its centre of mass and a pure rotation around the CM.

Friction will decelerate translation. The torque of friction accelerates rotation.

Try to write the equations of motion both for translation and rotation.

ehild

 

[j126]

That is where I got stuck. I've attempted several different equations that don't seem to lead to anything significant.

 

[ehild]

Newton's second law for the translation?

ehild