Snooker ball rolling, frictional effects, moment of inertia.

[karnten07]

Homework Statement

A billiard ball (of mass m and radius a) is struck by a cue and moves off with initial speed u, sliding (without rotation) along the table top. After what time will the ball roll rather than skid, if the frictional force between the ball and the table has magnitude qmg. (Recall that the moment of inertia of the ball about a diameter is 2/5 ma^2)

Homework Equations

The Attempt at a Solution

I see at the point when the ball begins to roll the ball will have an acceleration corresponding to a force that is less than the frictional force between the ball and table. But I am unclear on how to proceed on finding the time at which this occurs and where the moment of inertia comes into this. Any guidance much appreciated.

 

[karnten07]

its ok i think i got this one, found it here: http://www.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_4.html

 

[ogb p]

I would approach this problem by first understanding the concept of friction and how it affects the motion of an object. In this case, the frictional force between the ball and the table is what ultimately causes the ball to roll instead of slide.

To find the time at which the ball starts to roll, we need to consider the forces acting on the ball. The initial force acting on the ball is the cue's strike, which gives the ball an initial speed u. As the ball moves along the table, the frictional force acts in the opposite direction, slowing down the ball's motion.

At some point, the frictional force will become greater than the initial force, causing the ball to rotate instead of slide. This is when the ball starts to roll. To determine the time at which this occurs, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration (F=ma). In this case, the net force is the difference between the initial force and the frictional force.

We can also use the equation for the moment of inertia (I=2/5*ma^2) to relate the angular acceleration of the ball to its linear acceleration. This is because the moment of inertia is a measure of an object's resistance to rotational motion.

By setting the net force equal to the frictional force and using the equation for the moment of inertia, we can solve for the acceleration of the ball. Then, using the equation v=u+at, we can find the time at which the ball starts to roll.

In conclusion, the moment of inertia comes into this problem by relating the linear and angular acceleration of the ball. By considering the forces acting on the ball and using equations for motion and moment of inertia, we can determine the time at which the ball starts to roll instead of slide.