The rate at which an object's angular displacement changes as it rotates around a fixed point or moves along a circular path is known as its angular velocity. It is commonly expressed in radians per second (rad/s) or degrees per second (°/s) and is represented by the Greek letter omega (ω).

>>>>>(Angular Velocity Calculator using Angle and Time)

Whereas, linear velocity defines the speed at which an object's linear displacement changes with respect to time. It expresses the speed at which an object travels in a straight line.

Formula of Angular Velocity Calculator Using Linear Velocity

The following formula shows how linear velocity and angular velocity are related to one another:

v = r × ω

Where:
  • v is the linear velocity
  • ω is the angular velocity
  • r is the radius of rotation

So from the above formula of linear velocity we can easily get the angular velocity :

ω = v / r

Units of Angular Velocity :

  • Radians per Second (rad/s)
  • Degrees per Second (°/s)
  • Revolutions per Minute (RPM)

How Angular Velocity Calculator Using Linear Velocity Works: A Step-by-Step Example

Question :

A car is moving along a circular track with a radius of 15.5 meters. The linear velocity of the car is measured to be 11.22 meters per second. Calculate the angular velocity of the car in radians per second.

Solution :

Using the formula for angular velocity ω = v / r , where v is the linear velocity and r is the radius of rotation, we can substitute the given values:

ω = 11.22 / 15.5
ω = 0.723871 rad/s
So, the angular velocity of the car is 0.723871 radians per second.

Why to use our Angular Velocity Calculator Using Linear Velocity?

Our Angular Velocity Calculator helps you find out how fast something is spinning. Just enter the speed it's moving in a straight line and how far it is from the center. It quickly tells you how fast it's spinning around in circles. Easy to use and accurate, it's perfect for learning about spinning objects or solving real-world problems involving rotation.