- #1

AFlyingKiwi

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**1. Homework Statement**

A spherical billiard ball of uniform density has mass m and radius R and moment of inertia about the center of mass ( ) 2 cm I = 2/ 5 mR^2 . The ball, initially at rest on a table, is given a sharp horizontal impulse by a cue stick that is held an unknown distance h above the centerline (see diagram below). The coefficient of sliding friction between the ball and the table is µk . You may ignore the friction during the impulse. The ball leaves the cue with a given speed v0 and an unknown angular velocity ω0 . Because of its initial rotation, the ball eventually acquires a maximum speed of 9 / 7 v0 . The point of the problem is to find the ratio h / R.

## Homework Equations

L=Iw

p=mv

L_i = L_f

## The Attempt at a Solution

I have the solution in this link (http://web.mit.edu/8.01t/www/materials/InClass/IC-W15D2-5.pdf) but I don't get a certain part of it. When they give us initial L, it says L_i = mv_0(R) + I_cm(w_0). Why is the mv_0(R) there? Also, why can we use conservation of angular momentum if there is a net external force?