The ratio of angular speeds of the minute hand and the hour hand of a watch is:

Identify the increasing order of the angular velocities of the following:
$1$. Earth rotating about its own axis
$2$. Hour hand of a clock
$3$. Second hand of a clock
$4$. Flywheel of radius $2 \ m$ making $300 \ rpm$

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 $\text{m/s}$):

$A$ body rotating with an angular speed of $600 \, rpm$ is uniformly accelerated to $1800 \, rpm$ in $10 \, s$. The number of rotations made in the process is ..... .

$A$ wheel rotating at an angular velocity of $1200 \ rpm$ is slowed down at a constant angular acceleration of $4 \ rad \ s^{-2}$. How many revolutions will the wheel make before coming to rest?

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