What is the ratio of the angular speed of the minute hand to the hour hand of a clock?

If the equation for the displacement of a particle moving on a circular path is given as $\theta = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2$ seconds will be ....... $rad/sec$.

The wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

$A$ wheel undergoes a constant angular acceleration from time $t=0$ to $t=20 \ s$ and thereafter angular acceleration is zero. If angular velocity at $t=2 \ s$ is found to be $5 \ rad/s$, then the number of revolutions made by the wheel in the time interval $t=0 \ s$ to $t=50 \ s$ is

How many revolutions must a wheel complete to attain an angular velocity of $20 \, rad/s$ in $5 \, s$ starting from rest?

$A$ disc,initially at rest,is rotated about its axis with a uniform angular acceleration. In the first $2 \ s$,it rotates through an angle $\theta$. In the next $2 \ s$,the disc will rotate through an angle: