A disc of mass 2 kg and radius 0 . 2 m is rotating with an angular velocity 30 rad s - 1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0 .25 kg is stuck on th

Question

A disc of mass 2 kg and radius 0 . 2 m is rotating with an angular velocity 30 rad s - 1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0 .25 kg is stuck on the periphery of the disc, then its angular velocity will become

TestHub · Accepted Answer

When there is no external torque then the angular momentum remains constant.

i.e. $τ = 0 \Rightarrow \frac{d L}{d t} = 0$

$∴ I_{1} ω_{1} = I_{2} ω_{2}$ ... (i)

Here $M = 2 kg, m = 0.25 kg, r = 0.2 m,$

$ω_{1} = 30 rad s^{- 1}$

Hence, putting the value of $ω_{1}$ in equation (i), we get

$\Rightarrow \frac{1}{2} \times 2 \times {(0.2)}^{2} \times 30 = \frac{1}{2} \times (2 + 2 \times 0.25) {(0.2)}^{2} \times ω_{2}$

$\Rightarrow 1.2 = 0.05 ω_{2}$

$\Rightarrow ω_{2} = 24 rad s^{- 1}$

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