Angular Momentum Problem (from Giancoli)

[bobblo]

Homework Statement

On a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v0 and a "reverse" spin of angular speed w0. A kinetic friction force acts on the ball as it initially skids across the table. Using conservation of angular momentum, find the critical angular speed, ωC, such that if ω0 = ωC, kinetic friction brings the ball to a complete stop.

Homework Equations

L = r x p , L = Iω , and L = spin angular momentum + orbital angular momentum

The Attempt at a Solution

using L = spin angular momentum + orbital angular momentum (derived earlier), L = (2/5mR²)ωC - mv0r, where r is the distance from the origin, O, and R is the radius of the billiards ball. L is constant because no net external torque acts on the ball after it is hit, so i can solver for ωC: ωC = 5v0r/2R².

I checked the solution in the solutions manual, and it is reduced to 5v0/2R. I do not know why r = R, or orbital angular momentum depends on the radius of the ball, rather than the distance from the origin.

Thanks in advance.

 

[Tanya Sharma]

The Attempt at a Solution

using L = spin angular momentum + orbital angular momentum (derived earlier), L = (2/5mR²)ωC - mv0r, where r is the distance from the origin, O, and R is the radius of the billiards ball. L is constant because no net external torque acts on the ball after it is hit, so i can solver for ωC: ωC = 5v0r/2R².

I checked the solution in the solutions manual, and it is reduced to 5v0/2R. I do not know why r = R, or orbital angular momentum depends on the radius of the ball, rather than the distance from the origin.

Thanks in advance.

r = perpendicular distance from the origin