The relative angular speed of the hour hand and minute hand of a clock is (in $rad/s$):

$A$ 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:

If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$,then its linear velocity is (in $\text{m/s}$):

$A$ flywheel starts from rest and rotates with a constant angular acceleration of $3.0 \ rad/s^2$. An observer notes that it covers an angle of $120 \ rad$ in a time interval of $4.0 \ s$. How long had the wheel been rotating before the observer started the observation?

The velocity $\vec{v}$ of a particle of mass $m$ acted upon by a constant force is given by $\vec{v}(t) = A[\cos(kt) \hat{i} - \sin(kt) \hat{j}]$. Then the angle between the force and the velocity of the particle is (Here $A$ and $k$ are constants). (in $^{\circ}$)

$A$ wheel rotates with a constant angular acceleration. The initial angular velocity is zero. It covers an angular displacement of ${\theta _1}$ in the first $2 \, s$ and ${\theta _2}$ in the next $2 \, s$. Then,the ratio $\frac{{\theta _1}}{{\theta _2}}$ is equal to: