Difference Between Linear Velocity And Angular Velocity

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Velocity is a rate of change of the position of an object within a certain time range. There are two different types of velocity: angular velocity and linear velocity. Linear velocity is the rate of change of the position of an object that is traveling along a straight path. Any object that moves has a linear velocity. On the other hand, angular velocity only applies to objects moving along a circular path. Angular velocity is the rate of change of the angular displacement over time.

What is Angular Velocity?

Angular velocity is the rate of velocity at which an object or a particle is rotating around a center or a specific point in a given time period. Angular velocity is measured in angle per unit time or radians per second (rad/s). The rate of change of angular velocity is angular acceleration.

To understand angular velocity, you need to understand what rotation is. To help you with your understanding, let us consider a windmill. A windmill is a rigid body that rotates about a fixed axis. A windmill exhibits rotational motion when the blades of the windmill rotate around an axis that passes through the rotor. The velocity associated with rigid bodies as they exhibit rotation about a fixed axis is called angular velocity.

The symbol used for angular velocity is usually a lower case Greek symbol omega, ω. Angular velocity is represented in units of radians per time or degrees per time (usually radians in physics).

What is Linear Velocity?

Velocity denotes the distance that a moving body travels in a specific direction in a given amount of time. Linear velocity is simply an object’s velocity in a straight line. It is given as the ratio of distance covered to time. Denoted using V or Vl and measure using SI unit m/s. It is a vector quantity.

The linear velocity depends on the distance travelled by an object with respect to time taken. The linear equation or the linear velocity formula is given by,

v = x/t

Where,

  • v = Linear velocity
  • x = distance covered
  • t = Time taken to cover the distance(x).

How do you convert angular velocity to linear velocity?

Divide the linear velocity by the circumference to get the angular velocity (in rotations per unit time, which you can then convert to whatever other unit you are interested in). Multiply the angular velocity (in rotations per unit time – convert first if you need to) by the circumference to get the linear velocity.

Also Read: Difference Between Speed And Velocity

Conclusion

Linear and angular velocities are related to the speed of an object based on the perspective chosen. Linear velocity is applied to an object that moves, whereas angular velocity applies to those that turn such as a wheel, the earth’s revolution or a spinning top.

Angular velocity plays an eminent role in the rotational motion of an object. The linear velocity of every participating particle is directly related to the angular velocity of the whole object.

These two end up as vector products relative to each other. Basically, the angular velocity is a vector quantity and is the rotational speed of an object. The angular displacement of in a given period of time gives the angular velocity of that object.