# What controls whether a ball will skid or roll?

A billard ball is struck with a cue. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity $v_0$ of the ball, its radius $R$, its mass $M$ and coefficient of friction $\mu_k$ between the ball and the table are all known. How far will the ball move before it ceases to slip on the table?

• This looks very like a homework question, and the site rules forbid us from answering homework questions. If you want to edit your question to make it more general e.g. "what controls whether a ball will skid or roll?" we can answer that, but to be honest you could easily Google for that answer. Commented Jul 18, 2012 at 12:02
• I could not find an answer for this question. I'm editing the question now. Commented Jul 18, 2012 at 12:06
• See real-world-physics-problems.com/physics-of-billiards.html under the heading "A Closer Look At Relative Slipping" Commented Jul 18, 2012 at 12:17

Depending on your convention (what is positive or negative) you need an expression for the slip amount based on the ball linear speed $v(t)$ and rotational speed $\omega(t)$. What you are after is the instance these two give zero slip.