Question

A wheel starting from rest is uniformly accelerated at 4 rad/s² for 10 seconds. It is allowed to rotate uniformly for the next 10 seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

Answer 1

It is given that the area under the $\omega -t$ curve gives the total angular displacement.
∴ Maximum angular velocity = $\omega =\alpha t$
$\omega =4\times 10=40\mathrm{rad}/\mathrm{s}$



Area under the curve
$$\begin{gathered} =\frac{1}{2}\times 10\times 40+40\times 10+\frac{1}{2}\times 40\times 10 \\ =800\mathrm{rad} \end{gathered}$$
∴ Total angle rotated in 30 s = 800 rad.