$A$ body is revolving with a uniform speed $v$ in a circle of radius $r$. The tangential acceleration 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 $300 \ rpm$

Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ is:

Three particles $A, B$ and $C$ move in a circle of radius $r = \frac{1}{\pi} \, m$ in the anticlockwise direction with speeds $1 \, m/s$,$2.5 \, m/s$ and $2 \, m/s$ respectively. The initial positions of $A, B$ and $C$ are as shown in the figure. The ratio of the distance travelled by $B$ and $C$ by the instant $A, B$ and $C$ meet for the first time 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?

$A$ 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?