What is Tangential Velocity? - Definition & Formula

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  • 0:05 Describing Velocity & Speed
  • 1:17 Equation
  • 1:30 Other Equation Forms
  • 4:34 Lesson Summary
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Lesson Transcript
Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson, we define tangential velocity in terms of the radius of a circle and the time needed to make one complete revolution of the circle. We then extend this definition to include frequency and angular frequency.

Describing Velocity and Speed

From physics, we define a vector as a quantity having both magnitude and direction. For example, velocity is a vector where the magnitude is the speed. And speed is distance divided by time. What about the direction? For tangential velocity, we are describing the motion along the edge of a circle and the direction at any given point on the circle is always along the tangent line. Because of this understanding of tangential direction, we use the words ''tangential velocity'', but our equation will be calculating the speed.

Imagine a circle of radius r. Sitting on the edge of the circle, how far have we gone in one complete revolution? Answer: a distance given by 2πr. Sure, this distance is the same as the circumference of the circle. Also, we don't have to be on the edge of the circle. We can talk about the tangential velocity of any point r units from the center of a circle.

Tangential velocity, v

Are you familiar with the concept of a period of revolution? This is the time required to make one complete revolution. We usually use the letter T for the period.

We are now ready to give an equation for the tangential velocity.


As an equation, the tangential velocity is the distance, 2πr, divided by the time, T. Thus,


A point on the circle moves a distance 2πr in a time T.

Other Equation Forms

We can extend our equation by looking at a few ideas. These concepts include the angular speed, ω, and the frequency, f.

  • The angular speed, ω, is a speed of rotation. It measures the number of radians (or degrees) per second. Note, other names for angular speed include angular frequency and circular frequency.
  • Another measure of rotation per second is the frequency, f. There is an important difference, however. The frequency is the number of cycles per second. A cycle refers to one complete revolution where we are back at the starting point.

For the example, if we do 2 complete revolutions in 1 second, the frequency is 2 cycles per second.

How are ω and f related?

  • The angular frequency is 2π times the frequency.


ω is usually in radians per second. Every time we complete 2π radians of rotation, we have made one complete cycle around the circle. Thus, ω divided by 2π is the number of cycles per second. The number of cycles per second is the frequency. Thus, ω/(2π) = f and ω = 2π f.

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