A solid cylindrical pulley of mass m and radius `R = 10 cm` is hinged about its horizontal axis of symmetry. A light spring is wrapped around it, and small block of mass 'm' is suspended from the string. Now the block is lefted vertically by a distance h = 1.8 m and released. Just after the string becomes taut again, find the angular velocity of the cylinder in rad/s (Take `g = 10 m//sec^(2)`)

Answer

40

Explanation

Applying angular momentum conservation about the hinge point, between just before and just after the jerk
`L_(i) = L_(f)`
`(m) (sqrt(2gh)) (R ) = (m) (omegaR) (R ) + ((mR^(2))/(2)) omega`
`omega = (2)/(3) (sqrt(2gh))/(R ) rarr omega = (2)/(3) (sqrt(2 xx 10 xx 1.8))/(0.1)`
`omega = 40 "rad"//sec`