The linear speed of the tip of the seconds hand of a wall clock is $1.05 \, cm \, s^{-1}$. The length of the seconds hand is nearly ........ $cm$.

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 $300 \ rpm$

The relative angular speed of the hour hand and the second hand of a clock is:

$A$ wheel of radius $30 \ cm$ is driven by a belt. Its initial angular speed is $2 \ rev/s$. Starting at this speed,it comes to rest after a length of $25 \ m$ of the belt has passed over the wheel. The angular deceleration of the wheel is ....... $rad \ s^{-2}$.

The angular speed of a flywheel is increased from $600 \text{ rpm}$ to $1200 \text{ rpm}$ in $10 \text{ s}$. The number of revolutions completed by the flywheel during this time is :

$A$ particle at rest starts moving with a constant angular acceleration of $4 \ rad/s^2$ in a circular path. The time at which the magnitudes of its centripetal acceleration and tangential acceleration will be equal is (in seconds):