Question

A 66 nm torque acts on a wheel with a moment of inertia of 175 kg m2. if the wheel starts from rest, how long will it take the wheel to make one revolution?

Answer 1

Answer: 5.8 s

Explanation:

Newton's second law for rotational motions states that:

$\tau=I \alpha$

where

$\tau$ is the net torque

I is the moment of inertia

$\alpha$ is the angular acceleration

Substituting data and re-arranging the equation, we find the angular acceleration:

$\alpha=\frac{\tau}{I}=\frac{66 Nm}{175 kg m^2}=0.38 rad/s^2$

Now we can use the SUVAT equation for rotational motions:

$\theta(t)=\frac{1}{2}\alpha t^2$

where

$\theta(t)=2 \pi$ is the angle corresponding to one revolution

t is the time taken

Re-arranging the equation:

$t=\sqrt{\frac{2 \theta}{\alpha}}=\sqrt{\frac{2(2\pi)}{0.38 rad/s^2}}=5.8 s$