Question

A wheel starting from rest is uniformly accelerated at 4 rad/s${}^2$ 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

Area under the curve will decide the total angle rotated :

$\therefore$ Maximum angular velocity = 4 $\times$ 10 = 40 rad/s Therefore, Area under the curve

=$\frac{1}{2}\times 10\times 40+40\times +\frac{1}{2}\times 40\times 10$

=800 rad

$\therefore$ Total angle rotated = 800 rad.