A billiard ball of mass m and radius r, when hit ina horizontal direction by a cue at a height h above its centre, acquired a linear velocity v. Find the angular velocity w acquired by the ball.
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The angular velocity w acquired by the ball is ω = 5voh / 2r^2 .
Explanation:
We know that:
The effect of force FF lies at high hh.
Torque τ = I x α
I = m x v₀
F⋅h= 2/5 mr^ 2 ⋅ ω/t [∵α= ω/t ]
m⋅ah= 2/5 mr^2 ω/t
m⋅ v 0 / t . h = 2/5 mr^2 ω/t
ω = 5voh / 2r^2
Hence the angular velocity w acquired by the ball is ω = 5voh / 2r^2 .
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