Question

A wheel starting from rest is uniformly accelerated at $4rad/s^2$ for $10s$. It is allowed to rotate uniformly for the next $10s$ and is finally brought to rest in the next $10s.$ The total angle rotated by the wheel is $\theta$ (in rad). Find the value of $\frac{\theta }{100}$.

Answer 1

$\omega =\alpha \times t=4\times 10=40rad$

$\theta =$ Area under $\omega -t$ graph ....(1)

$=\frac{1}{2}(10\times 40)+(10\times 40)+\frac{1}{2}(10\times 40)$
$=800rad$