# Sliding time before a ball begins to roll on a horizontal surface

1. Jun 8, 2014

### NZBRU

1. The problem statement, all variables and given/known data

A ball is released along a horizontal surface with a co-efficient of friction Us at a speed V. Find the time it takes for the ball to start rolling (leave the moment of inertia as I).

2. Relevant equations

Quite a few, all of them are stated in my working (that I believe are relevant).

3. The attempt at a solution

2. Jun 9, 2014

### Simon Bridge

What is your reasoning?

3. Jun 9, 2014

### NZBRU

After reviewing my lecture notes I found that I copied down a different solution. I attempted to redo the problem but came up with this solution, I must of either copied the answer incorrectly or made a mistake in the above working.

In regards to reasoning The Torque net must be equal to the frictional force acting directly below the ball multiplied by the radius, R. I assumed that the initial rotational velocity was zero. Using Torque(net) = I x alpha I found an expression for alpha. As the initial rotational velocity was equal to zero alpha = w/t.

I made the assumption that then the ball stopped rolling, V=Rw and solved for V. Using the kinematic equation v = u + at I solved for u (the initial linear velocity) and then solved for t.

Last edited: Jun 9, 2014
4. Jun 9, 2014

### ehild

Your method and result are both correct. Be careful with the signs, sometimes you wrote them incorrectly. The friction accelerates rotation but decelerates translation: Initially the ball slides, so α=dω/dt=μmg/I, ω=μmgt/I. μ is the coefficient of kinetic friction. At the same time, friction decelerates the translational motion of the CM: a=-μg, v=v0-μgt.

ehild