Question

A uniform disc of radius ' a' and mass 'm' is rotating freely with angular speed 'ω' in a horizontal plane, about a smooth fixed vertical axis through its centre. A pa1ticle of mass 'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular speed is ______

Options

• `ω/sqrt3`

• `ω/sqrt5`

• `ω/3`

• `ω/5`

Answer 1

A uniform disc of radius ' a' and mass 'm' is rotating freely with angular speed 'ω' in a horizontal plane, about a smooth fixed vertical axis through its centre. A pa1ticle of mass 'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular speed is `underline(ω/3)`.

Explanation:

L_i = `1/2"ma"^2omega`

`"L"_"f" = 1/2"ma"^2omega^' + "ma"^2omega^' = 3/2"ma"^2omega^'`

∵ L_i = L_f ........by conservation of angular momentum.

∴ `1/2"ma"^2omega = 3/2"ma"^2omega^'`

∴ ω = 3ω'

∴ ω' = `ω/3`