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Angular Speed Calculator
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Angular speed is the distance covered in the circular path in the given time. In short it is the scalar measure of rotation rate.It differs by linear speed as it travels in a circular path instead of linear path.It is given by
$\omega$ = 2 $\pi$ f
Where $\omega$ = Angular speed and
f = frequency

The frequency is the number of rotations taken in the given time. Hence it is given by
f = $\frac{1}{T}$
Where T = time taken.

Angular speed Calculator
helps to calculate the frequency if angular speed is given and vice-versa. It also calculates the linear speed, angular or radius of circular path if any of the two quantities are given.

Steps for Angular Speed Calculator

Step 1 :

Go through the problem and observe the given parameters.

Step 2 :

If frequency is given

Use the formula:

$\omega$ = 2 $\pi$ f

where $\omega$ = angular speed and

f = frequency taken

and if linear speed and radius of circular path is given

$\omega$ = $\frac{V}{r}$

where  V = Linear speed and

r = radius of circular path

Substituting the given values we get the desired parameter.

Problems on Angular Speed Calculator

1. A wheel of 0.60m in radius is moving with a speed of 10m/s. Find the angular speed.

Step 1 :

Given:

Linear speed V = 10 m/s

radius of wheel r = 0.6 m

Step 2 :

Using the formula:

$\omega$ = $\frac{V}{r}$

$\omega$ = $\frac{10 m/s}{0.6 m}$

The angular speed $\omega$ = 16.67 rad/s

2. The angular speed of a giant wheel ia 20 rad/s. Calculate its frequency.

Step 1 :

given: $\omega$ = 20 rad/s,

frequency f = ?

Step 2 :

Use the formula:

$\omega$ = 2 $\pi$ f
$\therefore$ f = $\frac{\omega}{2 \pi}$
f = $\frac{20 rad/s}{2 \pi}$