Any body in circular path covers certain angle from center taken as fixed axis. The distance is expressed in angles as there will be twist in the position.
The angular motion is the rotatory motion that a body takes when all the points on a body or object moves in circles about the central line or axis. Lets see more about this. Vehicles in angular motion |

Lets us take a body moving in a circular path having initial angle

**$\theta_o$**after some time it undergoes displacement**$\theta$**covering the distance with angular velocity**$\omega$**from its initial angular velocity**$\omega_o$**. The angular acceleration related to it is**$\alpha$**.

**They are many equations in angular motion. Here are some equations:**

**$\omega = \omega_o + \alpha\ t$**

$\theta$ = $\frac{1}{2}$ ($\omega_o + \omega$) t

$\theta$ = $\omega_o$ t + $\frac{1}{2}$ $\alpha$ t2

$\omega^2$ = $\omega_o^2$ + 2 $\alpha$ $\theta$Here

$\theta$ = $\frac{1}{2}$ ($\omega_o + \omega$) t

$\theta$ = $\omega_o$ t + $\frac{1}{2}$ $\alpha$ t2

$\omega^2$ = $\omega_o^2$ + 2 $\alpha$ $\theta$

**$\theta$**is the angle change,

**$\theta_o$**is the initial angular position,

**$\omega$**is the angular velocity,

**$\omega_o$**is initial angular velocity at t,

**$\alpha$**is the angular acceleration.

Angular projectile motion is the angle that the projectile makes with the horizontal surface.

**v cos $\theta$**

Vertical component in terms of $\theta$ is

**v sin $\theta$**.

If a body is moving in a circular path maintains constant acceleration

**$\alpha$**. The angular motion equations are**$\alpha$ = Constant**

$\omega$ = $\omega_o$ + $\alpha$ t

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

$\omega$ = $\omega_o$ + $\alpha$ t

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

^{2}Here

**$\theta$**is the angle change,

**$\theta_o$**is the initial angular position,

**$\omega$**is the angular velocity,

$\omega_o$ is initial angular velocity at t,

$\alpha$ is the angular acceleration.

Angular acceleration

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**($\alpha$)**also known as rotational acceleration is the change in velocity of angular velocity with time. Its a vector quantity and is expressed in radians per second**(rad s**.^{-2})That tells us that angular acceleration is a rate of change of angular velocity

**$\omega$**.Angular velocity decides what rate the body is moving in a circular path. It is the rate of change of angular displacement with time. It is given as

**$\omega$**is the angular velocity

**$\theta_f$**is the final angular displacement

**$\theta_i$**is the initial angular displacement

**t**is the time taken.

**angular displacement**is!

If

**S**is the angular displacement and**$\theta$**is change in angle. The angular displacement isAngular speed ($\omega$) is that what decides how fast a body is changing its position in a circular path. Its the ratio of what's the change in angular position to how much time it takes. It is given by

Here

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**$\theta$**is the angle change and**t**is the time taken.**Here are given some simple examples of angular speed:**

### Solved Examples

**Question 1:**What is the angular speed of

**Seconds hand and (b) Minute hand of a clock.**

**(a**)**Solution:**

Given : Angular displacement $\theta$ = 2 $\pi$ radians,

Time taken t = 60 s

The angular speed of second hand is

$\omega$ = $\frac{\theta}{t}$

= $\frac{2 \pi}{60}$

= 0.1047 rad s

= $\frac{2 \pi}{60}$

= 0.1047 rad s

^{-1}.The angular speed of minutes hand is

$\omega$ = $\frac{\theta}{t}$

= $\frac{2 \pi}{3600}$

= 0.001745 rad s

= $\frac{2 \pi}{3600}$

= 0.001745 rad s

^{-1}.**Question 2:**A wheel of radius 0.5 m rotates at 500 rpm. Calculate the angular velocity in rad s

^{-1}.

**Solution:**

Given: Radius of wheel = r = 0.5 m,

Frequency of revolution f = 500 rpm = 8.33 rps

The angular velocity is

$\omega$ = 2 $\pi$ f

= 2 $\times$ $\pi$ $\times$ 8.33 rps

= 16.66 $\pi$ rad s

$\omega$ = 2 $\pi$ f

= 2 $\times$ $\pi$ $\times$ 8.33 rps

= 16.66 $\pi$ rad s

^{-1}.