Question

a body whose moment of inertia is 3.0 kg/m2 is at rest. It rotated for 20 s by a torque of 6.0 Nm. Calculate the (i) angulardisplacement of the body in 20 s. (ii) angularmomentum of the body at 20 s. Is the angular momentum of the body constant ?„explain.(iii) work done by the torque.

Answer 1

Answer on Question #73764-Physics-Mechanics-Relativity

A body whose moment of inertia is $3.0 \, \mathrm{kg/m^2}$ is at rest. It rotated for 20 s by a torque of 6.0 Nm. Calculate the (i) angular displacement of the body in 20 s.

(ii) angular momentum of the body at 20 s. Is the angular momentum of the body constant? explain.

(iii) work done by the torque.

Solution

i)

$$\alpha = \frac{T}{I}$$ $$\theta = \frac{1}{2} \alpha t^{2} = \frac{1}{2} \left(\frac{6}{3}\right) (20)^{2} = 400 \, \text{rad}.$$

ii)

$$L = I \omega = I \alpha t = (3) \left(\frac{6}{3}\right) (20) = 120 \, \text{kg} \, \frac{\text{m}}{\text{s}}.$$

The angular momentum of the body is not a constant because angular acceleration is not a zero.

iii)

$$W = \frac{1}{2} I \omega^{2} = \frac{1}{2} (3) \left(\left(\frac{6}{3}\right) (20)\right)^{2} = 2400 \, J = 2.4 \, \text{kJ}.$$

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