Anybody moves along the circular path is termed as in rotational motion.It moves in the circular path with velocity and acceleration is quite different from the linear motion. Here come the angular motion, inertia and other concepts. The basic formulas in rotational motion are:

If $\omega$ is the angular velocity. The angular velocity is,
$\bar{\omega}$ = $\frac{\Delta \theta}{\Delta t}$.

Angular acceleration is,
$\bar{\alpha}$ = $\frac{\Delta \omega}{\Delta t}$.

Velocity of rotational motion is,
v = r $\omega$.

There are a lot more equations in rotational motion. Some of them are,
$\omega(t)$ = $\omega_o(t)$ + $\alpha$ t

$\theta$ = $\theta_o$ + $\omega_o$ t + $\frac{1}{2}$ $\alpha$ t$_{2}$

$\omega^2(t)$ = $\omega_o^2(t)$ + 2 $\alpha$ $\theta$

$\bar{\omega}$ = $\frac{\omega + \omega_o}{2}$.

Where $\omega_o$ and $\omega$ are initial and final angular velocity, $\alpha$ is angular acceleration, t is time taken.

Rotational Motion Examples

Below are given some examples of rotational motion:

Question 1: A body rotates in a circular path of radius 2 m with velocity 4m/s. Calculate the angular velocity.
Solution:

Given: velocity v = 4m/s, radius r = 2m

The angular velocity is,
$\omega$ = $\frac{v}{r}$

$\omega$ = $\frac{4m/s}{2m}$

$\omega$ = 2 rad/s.

Question 2: A disc rotates with angular acceleration of 10 rad/s2 in a fixed axis which is perpendicular passing through the center.Calculate the angular velocity after 5 seconds.
Solution:

Given: Angular acceleration $\alpha$ = 10 rad/s2, time t = 5 s, initial angular velocity $\omega_o$ = 0

The angular velocity is,
$\omega(t)$ = $\omega_o(t)$ + $\alpha$ t

$\omega(t)$ = 0 + (10 rad/s2) (5 s)

$\omega(t)$ = 50 rad/s.