- 130

- 0

**1. Homework Statement**

I got struck with this problem again in the review questions and still can't do it, I think this problem shows a major gap in my knowledge of the subject.

A solid ball of radius R is set spinning with angular speed [tex]\omega[/tex] about a horizontal axis. The ball is then lowered vertically with negligible speed until it just touches a horizontal surface and is released. If the coefficient of kinetic friction between the ball and the surface is [tex]\mu[/tex], find the linear speed of the ball once it achieves pure rolling motion and the distance it travels before its motion is pure rolling.

**2. Homework Equations**

[tex]W=\Delta K[/tex]

[tex]I_0\omega_0=I\omega[/tex]

[tex]I=\frac{2}{5}MR^2[/tex]

[tex]v=R\omega[/tex]

**3. The Attempt at a Solution**

Now i dont think i can use conservation of angular momentum because the external force of friction is acting on the ball, which brings me to another question...how can one use conservation of mechanical energy for a ball rolling down an incline? ie mgh=1/2 mv^2 + 1/2I[itex]\omega ^2[/itex]

To solve this problem i would probably say

[tex]-\frac{1}{2}I\omega^2+\frac{1}{2}I\omega_f ^2 + \frac{1}{2}MR^2\omega_f ^2=F_fs[/tex]

but i dont think i can use [tex]F_f = \mu Mg[/tex]

and i am not given how far the ball slips before its in pure rolling motion (actually its asked int he question to find that) so i dont think i have enough information to solve this problem.