Question

‏A 50 - N x m torque acts on a wheel with a moment of inertia 150 kg x m² . If the wheel starts from rest , how long will it take the wheel to make one revolution ?

Answer 1

Answer:

t = 6.17 s

Explanation:

For a 1 revolution movement, $\triangle \theta = 2\pi$

Torque, $\tau = 50 Nm$

Moment of Inertia, $I = 150 kg m^2$

If the wheel starts from rest, $w_{0} = 0 rad/s$

The angular displacement of the wheel can be given by the formula:

$\triangle \theta = \omega_0 t + 0.5 \alpha t^2$................(1)

Where $\alpha$ is the angular acceleration

$\tau = I \alpha\\\alpha = \frac{\tau}{I} \\\alpha = 50/150\\\alpha = 0.33 rad/s^2$

To get t, put all necessary parameters into equation (1)

$2\pi = 0(t) + 0.5(0.33)t^2\\2\pi =0.5(0.33)t^2\\t^2 = \frac{4 \pi}{0.33} \\t^2 = 38.08\\t = 6.17 s$