# Billiard ball rotating and slipping

• aldee11
Therefore, you need to use these velocities in the equations for kinetic energy to find the work lost to friction.
aldee11
. Homework Statement
A ball radius "a" and mass "m" initially spinning counterclockwise with angular speed w=-v0/a with a forward speed vo. The coefficient kinetic friction between the ball and the billiard table is Mu, [Given a,m,vo,mu]
Determine the work lost to friction while slipping using two methods (they should be equal)
W=-Ffs where s the distance ball slips not travels
W= delta Kt + delta Kr

2. Homework Equations
F=ma
Torque= I*alpha
W=v/r
V=vo+at
W=Wo+alpha*t

3. The Attempt at a Solution

I found a from equation F= ma where F=-Ff
Then plug in a to eq V=Vo+at

I also found alpha from eq Torque= I alpha
then plug in alpha to eq W=Wo+ alpha t

set V=RW i got T where the slipping becomes rolling without slipping.

The questions are
1. Can i use this t and plug it into eq X=Xo+Vot+0.5at^2 to find The distance the ball SLIPS??
2. If i can't use that equation, then How can i find the distance the ball slips?
3. In finding W= delta Kt + delta Kr, Do I have to use final angular and forward speed that i found from previous calculation or Do i have to find them?

Dear forum post author,

1. Yes, you can use the equation X=Xo+Vot+0.5at^2 to find the distance the ball slips. However, you need to make sure that the acceleration a you use is the tangential acceleration of the ball as it slips, not the linear acceleration. This can be found by taking into account both the frictional force and the tangential component of the ball's weight.

2. Alternatively, you can use the equation W=Fd to find the distance the ball slips, where F is the frictional force and d is the distance over which the force acts. This distance can be found by considering the fact that the ball starts with an initial linear velocity and ends with an angular velocity due to rolling without slipping.

3. To find the work lost to friction using the method W= delta Kt + delta Kr, you need to use the final angular and linear velocities that you have calculated. These velocities represent the change in kinetic energy due to the slipping and the rolling without slipping, respectively.

## What is the difference between rotation and slipping in a billiard ball?

Rotation refers to the circular motion of a billiard ball around its center, while slipping refers to the translation or movement of the ball across the surface it is rolling on. In other words, rotation is the spinning motion of the ball, while slipping is the movement of the ball as a whole.

## Why do billiard balls sometimes slip instead of roll?

Billiard balls can slip instead of roll due to a lack of friction between the ball and the surface it is rolling on. This can happen if the surface is too smooth, if the ball is moving too fast, or if there is moisture or debris on the surface that reduces friction.

## How does the weight of a billiard ball affect its rotation and slipping?

The weight of a billiard ball can affect its rotation and slipping by influencing the amount of friction between the ball and the surface it is rolling on. A heavier ball will have more momentum and may require more force to start rotating, but it may also have more friction and be less likely to slip.

## What factors can impact the speed of rotation and slipping in a billiard ball?

The speed of rotation and slipping in a billiard ball can be impacted by several factors, including the weight and size of the ball, the surface it is rolling on, the force applied to the ball, and any external factors such as humidity or debris on the surface.

## How can a player control the rotation and slipping of a billiard ball?

A player can control the rotation and slipping of a billiard ball by adjusting the force and direction of their shot, choosing a cue with the right weight and tip, and maintaining a clean and smooth playing surface. They can also use techniques such as "english" or spin on the ball to control its rotation and slipping.

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