What is the difference between angular velocity and linear velocity

The words velocity and speed provide us with a sense of how quickly or slow an item is traveling in relation to our position. We run into instances when we need to determine which of two or more things is traveling quicker than the other. This happens very frequently. The velocity of an item is defined as the rate at which its position changes in relation to a reference frame and over time. It can be measured in meters per second ms The angular velocity of a particle is defined as the rate at which the angular displacement of the particle changes.

The linear velocity can be defined as the rate at which linear displacement changes over time. Angular and linear velocities are both present in everything that rotates or travels in a circle. For example, consider riding a merry-go-round. A stone thrown off the edge of a spinning merry-go-round will not fall straight down. Instead, it will continue to go ahead at the same speed that the merry-go-round was traveling at when the stone was thrown. While they differ in the aspect of scalar and vector.

Angular speed is a scalar quantity whereas the angular velocity is a vector quantity. First, speed is a scalar quantity. We will create a few useful and easy to use formulas, and see how they are all related. Then, together, armed with these formulas, we can see the affects of propeller on a plane, how two pulleys work together, like the one you find on a bike, and how the earth rotates about the sun or a satellite rotates about the earth.

Get access to all the courses and over HD videos with your subscription. Get My Subscription Now. At any moment, this relationship applies to every particle that has a rigid body. Linear Velocity. Angular Velocity. We define the linear velocity as the rate of change of the linear displacement. We define the angular velocity as the rate of change of angular displacement. Key Differences. In a circular motion, the linear velocity of a particle is along the circumference of a circle. It is different at different points on the circle.

The angular velocity of a particle is along the axis of a circle. It remains the same throughout the circular motion. The symbol for the linear velocity is v. The symbol for angular velocity is a Greek letter, i. It is an axial vector. Its because the direction of the displacement of the particle is along the axis of the circle. Measuring Unit. We measure the angular velocity in both degrees and radians.