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?

Obtain the equation $\omega = \omega_{0} + \alpha t$ from first principles.

$A$ ceiling fan starts from rest and makes $10$ revolutions in the first $3$ seconds. If the angular acceleration remains constant,how many revolutions will it make in the next $3$ seconds?

Three particles $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi} \, m$ in the anticlockwise direction with speeds $1 \, m/s$,$2.5 \, m/s$ and $2 \, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in the figure. The ratio of the distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time is

$A$ fan starts from rest and makes $10$ revolutions in the first $3$ seconds. Assuming constant angular acceleration,how many revolutions will it make in the next $3$ seconds?

If the length of the second's hand in a stop clock is $3 \, cm$,the angular velocity and linear velocity of the tip are: