$A$ clock has a continuously moving second's hand of $0.1\, m$ length. The average acceleration of the tip of the hand (in units of $m\, s^{-2}$) is of the order of

$A$ 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):

The ratio of the angular speed of a second-hand to the hour-hand of a watch is (in $: 1$)

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ 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 $300 \ rpm$

$A$ car wheel rotates at $1200$ revolutions per minute. On pressing the accelerator,it rotates at $4500$ revolutions per minute in $10 \ s$. The angular acceleration of the wheel is ...