As part of maintenance,a jet engine compressor is rotated as shown in the graph. What is the total number of revolutions made by the compressor during the given time interval?

$A$ particle is revolving in a circle of radius $2 \ m$ with angular velocity $\omega = t^2 - 4t + 8 \ rad/s$. The time when the speed of the particle becomes $8 \ m/s$ is ......... $\sec$.

$A$ body rotating with uniform angular acceleration covers $100 \pi \text{ rad}$ in the first $5 \text{ s}$ after the start. Its angular speed at the end of $5 \text{ s}$ (in $\text{rad/s}$) is .........$\pi$.

$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?

$A$ fan is rotating with an angular speed of $300 \text{ rpm}$. The fan is switched off,and it takes $80 \text{ s}$ to come to rest. Assuming constant angular deceleration,the number of revolutions made by the fan before it comes to rest is:

$A$ flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad/s$ to $40\pi \, rad/s$ in $10 \, s$. How many rotations did it make in this period?