Question

A solid sphere of mass `m` and radius R is hit by a cue at height `h` above the center of sphere. The cue applies a force `F` and the contact period is small time `t`. Find
(`a`) the velocity of center of mass,
(`b`) the angular speed of sphere about the center of mass and
(`c`) the value of `h` so that the sphere rolls without slipping after removal of force.

Answer 1

Linear impulse
`Ft=Deltap=m(v_(c.m.)-0)implies v_(c.m.)=(Ft)/(m)`
Angular impulse about `O`
`tau t=Delta L`
`Fht=I_(c.m.)(omega-0)`
`Fht=(2)/(5)mR^(2)omegaimpliesomega=(5Fht)/(2mR)`
For pur rolling.
`v_(c.m)=Romegaimpliesh=(2R)/(5)`