Angular Velocity Calculator

An online angular velocity calculator allows you to determine the angular velocity of the body in motion on a circular path. This angular speed calculator uses different angular speed equations to find velocity in three different ways including:

Angle difference.
Radial velocity.
Angular velocity and linear velocity.

Now, we are here going to discuss the angular speed formula, how to find it manually & different other related terms. Also, you can use the online velocity calculator that allows you to determine the velocity/speed of the moving object. Swipe on!

What is Angular Velocity?

The angular velocity refers to how fast an object is rotating or revolving in a circular path relative to another point. In simple words, the rate of change of its angular position is called the angular velocity. It is generally represented by a symbol $ω$ $(Omega)$ & measured in $rad/s$ $(radian per second)$.

For example:

Earth completes its one rotation around the sun in one day or $360$ degrees per day. Its angular velocity will be

$ω = \frac {360°}{24h} or ω = \frac{2ᴨrad}{86400s}$.

What are the Formulas for Angular Velocity?

The formulas for the calculations depending upon the input parameters are as follows:

For Angle Difference:

If you have angle and time, then the formula will be: $$ ω = \frac{α₂ - α₁}{t} = \frac {Δα}{t} $$

Where,

$α₁$ & $α₂$ are the angles on the circle.

$Δα$ is the angle difference

$t$ is the time in which change of angle occurs.

You can also try the online acceleration calculator that helps you to calculate the rate of change of velocity of an object with different formulas.

For Radial velocity:

For calculation when you have linear velocity and radius as input parameters, then the formula used is: $$ v = ω \times r $$

It can be rewrite in the form of angular velocity is: $$ ω = r \times \frac {v}{|r|^2} $$

Where,

$r$ is radius & $v$ is the linear velocity and all are vectors while $|r|$ is the absolute value of the radius.

For Angular Velocity and Linear Velocity:

Converting angular velocity to linear velocity and vice versa can easily be done by this online angular velocity calculator. The formula used for these conversions is: $$ v = r \times RPM \times 0.10472 $$

Where,

$v$ is linear velocity in $m/s$ $r$ is radius in meters & $RPM$ is angular velocity in (Round per minute).

What Are the Angular Velocity Units?

As it has many units, but the units used by this online angular velocity calculator are mentioned below:

$Rad/s$ (Radian Per Second): As from the formula, it tells us how big the rotation an object moves in specific time.
$RPM$ (Revolution Per Minute): By using it, you can come to know how fast a wheel is spinning.
$Hz (Hertz)$: Also used for frequency but rarely used in angular velocity. Similar to the RPM but it tells us the spinning in seconds while RPM tells in minutes.

Our online calculator uses following conversions to convert these unit into each other:

$$ 1 RPM = 0.10472 rad/s = 0.01667 Hz $$ $$ 1Hz = 6.283 rad/s = 60 RPM $$

How to Calculate Angular Velocity From Different Formulas Manually (Step-by-Step)?

The calculations become very easy with this online angular speed calculator. Here we have examples of each method manually. Read on!

Example 1:

If an object moves from an angle of $5 rad$ to $25 rad$ in $16$ seconds. Calculate angular velocity of the object?

Solution:

Here,

$α₁ = 5rad$

$α₂ = 25rad$

$t = 16sec$

So,

$Δα = α₂ - α₁$

$Δα = 25 - 5$

$Δα = 20rad$

$ω = \frac{Δα}{t}$

$ω = \frac {20rad}{16s}$

$ω = 1.25rad/s$

Example 2:

A Ferris wheel having a radius of $10 m$, moving with linear velocity of $35 m/s$. What is the angular speed in radian per second?

Solution:

Here,

$v = 35 m/s$

$r = 10m$

So,

$ω = r \times \frac {v}{|r|^2}$

$ω = 10 \times \frac {35}{|10|^2}$

$ω = 10 \times \frac {35}{100}$

$ω = \frac {350}{100}$

$ω = 3.5rad/s$

Example 3:

The object moves in a circle having radius $1.5 m$ and having RPM of $10$, then finds the linear velocity of the object?

Solution:

Here,

$r = 1.5 m$

$RPM = 10$

So,

$v = 1.5 \times 10 \times 0.10472$

$v = 15 \times 0.10472$

$v = 1.57 m/s$

Our online angular velocity calculator also uses the same formulas for calculating angular speed.

How to Find Angular Speed With Angular Velocity Calculator:

The free online angular speed calculator determines the accurate result of angular speed/velocity with different following methods:

Angle Difference.
Radial Velocity.
Angular Velocity & Linear velocity.

Inputs:

First of all, you have to choose the method from the dropdown of this tool from which you want to calculate the angular velocity.
Then, enter the data according to the selected method.
Once you fill in all the designated fields, time to hit the calculate button.

Outputs: The online tool shows:

Angular velocity in rad/s, degree, RPM & Hz.
Linear velocity in m/s, kmps, kmph, miles/s, miles/h.
Angle change.
Time in minutes & hours.
Radius in m, cm, ft, inches, yd.

Note: No matter what the method is, the online angular velocity calculator shows you the results according to the selected calculation parameter.

Frequently Ask Questions (FAQ’s):

Is angular velocity the same everywhere?

Yes, it is the same at every point on the axis of rotation when an object is moving in a circular path. The tangential velocity is directly proportional to its distance from the axis of rotation.

How do you find velocity without time?

If you have to know the velocity of the body at some point before it hits the ground, then use the distance of the fallen object in place of distance to ground in either equation. Then multiplying the feet per second with $0.68$ will determine the velocity in miles per hour.

What is Omega equal to?

Angular velocity/frequency (ω) measures the angular displacement in unit time. Its units are degrees. rad/s. Angular frequency is larger than regular frequency by

$2π. (ω=2π)$

So,

$1 Hz=6.28rad/s$.

Why is V=ѠR?

It's the equation to find the linear velocity when angular velocity & radius are known parameters. If the rotation period is $t$, then $ω= \frac {2ᴨr}{t}$.

End-Note:

The angular velocity is helpful to determine the rotation rate of an object or body with respect to an inertial frame of reference. This calculator helps you to calculate the velocity of the object moving in the circular path. Also, this tool work as a converter that allows you to convert the linear velocity to angular velocity & vice versa.

References:

From the source of Wikipedia : Angular velocity definition, formulas. From the site of courses.lumenlearning : Units for the rotating velocity. From authorized source of hyperphysics.phy : Basic rotational quantities and much more: