Question

A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquired a linear velocity v_(0). The angular velocity omega_(0) acquired by the ball is

Answer 1

Answer:

The effect of force F lies at high h.

Torque τ=Iα

$$F\cdot h=\dfrac { 2 }{ 5 } m{ r }^{ 2 }\cdot \dfrac { \omega  }{ t } $$              $$\left[ \because \alpha =\dfrac { \omega  }{ t }  \right] $$

$$m\cdot ah=\dfrac { 2 }{ 5 } m{ r }^{ 2 }\dfrac { \omega  }{ t } $$

$$m\cdot \dfrac { { v }_{ 0 } }{ t } h=\dfrac { 2 }{ 5 } m{ r }^{ 2 }\dfrac { \omega  }{ t } $$

ω=2r25v0h