Question

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?

Answer 1

Answer:

After 8.5 s

Explanation:

We can use the equivalent suvat equation for rotational motions to find the angular acceleration of the wheel:

$\theta = \omega_i t + \frac{1}{2}\alpha t^2$

where:

$\theta = 2\pi rad$ is the angular displacement covered during the first 6.0 s (the angle corresponding to one revolution)

$\omega_i=0$is the initial angular velocity

$\alpha$ is the angular acceleration

t = 6.0 s is the time

Solving for  $\alpha$,

$\alpha = \frac{2\theta}{t^2}=\frac{2(2\pi)}{6.0)^2}=0.349 rad/s^2$

Now we want to find instead the time t after which the wheel has completed two revolutions, so the time t at which

$\theta = 4 \pi$

Using again the same equation as before and solving for t, we find:

$t=\sqrt{\frac{2\theta}{\alpha}}=\sqrt{\frac{2(4\pi)}{0.349}}=8.5 s$