To get a billiard ball to roll without sliding from the start, the cue must hit the ball not at the center (that is, a height above the table equal to the ball's radius, r) but at exactly at a height of 2r/5 above the centre. Prove the result.(adsbygoogle = window.adsbygoogle || []).push({});

For a ball to roll without slipping, it must have tangential velocity twice that of its velocity of the centre of mass.

so tangengial speed = ωr

at the point where the wheel contact the surface must be at rest

vcm - ωr = 0

vcm = ωr

L=Iω = Ip/mr

p = Lmr/I

so for conversation of momentum

mvcmi = mvcmf + Lmr/I

Δvcm = Lr/I

I for a sphere = (2/5)mr^2

where r is where the ball needs to hit

Δvcm = L/(2/5)mr

(2/5)mΔvcm/L = r

(2/5)Δp/L = r

(2/5)r = r

these last few steps dont seem right?

are they? am i even correct up to there?

thanks

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# Homework Help: Angular Momentum of a billiard ball

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