Question

A rotating ball hits a rough horizontal plane with a vertical velocity v and angular velocity w. Given that the coefficient of friction is u and the vertical component of the velocity after the collision is v/2, find:

a) the angular velocity after collision;

b) the impulsive ground reaction during the collision

Joshi sir comment

on applying momentum impulse theorem along vertical

-mv+Ndt = mv/2       (1)

by angular momentum angular impulse theorem

2mωr2/5 - μNdtr = 2mω,r2/5       (2)By eq. (2) get angular velocity.

impulsive ground reaction = (Ndt)2+(μNdt)2by using eq. (1), solve it

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