Angular Speed of a Uniform Circular Disc Under Torque – Rankers Physics
Topic: Rotational Motion
Subtopic: Dynamics of Rotational Motion

Angular Speed of a Uniform Circular Disc Under Torque

A uniform circular disc of mass \(2\text{ kg}\) and radius \(100\text{ cm}\) (hinged at centre) is subjected to a constant torque of \(4\text{ Nm}\). If the disc was initially at rest, then its angular speed after \(4\text{ s}\) will be
16 rad/s
4 rad/s
2 rad/s
8 rad/s

Solution:

Moment of inertia \(I = \frac{1}{2} M R^2 = \frac{1}{2} \times 2 \times 1^2 = 1\text{ kg m}^2\). Angular acceleration \(\alpha = \frac{\tau}{I} = \frac{4}{1} = 4\text{ rad/s}^2\). Angular speed \(\omega = \alpha t = 4 \times 4 = 16\text{ rad/s}\).

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