Bowling ball and force of friction

[ducdat231]

Homework Statement

A bowling ball with radius (R) and mass (m)hit the ground and traveled a distance (d) before it started to roll due to the force of friction cause by the coefficient of friction (mu) between the ball and the lane.

Homework Equations

I=2/5mR^2
F=ma
torque=I*alpha
F(friction)=mu*F
v=w*alpha

The Attempt at a Solution

Express the distance d in term of R, m, v and mu.

 

[aim1732]

I suppose it is important that you know whether the ball as spinning or translating initially.

 

[ducdat231]

initially the ball was as translating but after traveled distance (d) it change to spinning due to the friction with the lane

 

[aim1732]

Then write the translation and rotation equations. The speed reduces and angular velocity increases to the point that they satisfy the condition for pure rolling. As soon as this is achieved friction ceases to act.