What Is Tangential Velocity?

Tangential velocity is the velocity, or speed in a given direction, of an object traveling in a circle times the radius of that circle. Velocity is similar to speed; however, it takes into account the direction the object is moving, whereas speed does not. Tangential velocity involves continual circular motion. This is quite different from linear velocity, for example, which measures objects traveling in a straight line.

Angular velocity is important to determining tangential velocity. Angular velocity measures how fast a wheel is spinning. This speed is multiplied by the radius of the wheel to yield the tangential velocity. Tangential velocity increases as the distance from the center of the circle increases.

A tangent is a line that touches a curve. When a wheel is resting on a road, the straight line of the road touching the wheel is tangent to the curve of that wheel. In tangential velocity, the tangent or straight line must be the same direction as the spin of the wheel.

Radius is a linear measurement from the center of a circle to the outer edge of the circle. The diameter of a circle is the distance across a circle, so the radius is exactly half the diameter. Since tangential velocity increases as radius increases, larger wheels spinning at the same speed as smaller wheels have greater tangential velocity.

Speed is the distance an object travels divided by time. In the circular motion of tangential velocity, the distance traveled is the circumference of the wheel. Circular motion is measured in revolutions per second, or how many times the circle goes around in one second. Interestingly, the speed and forces on a spinning wheel vary at different points on that wheel, and this is why tangential velocity is important.

The children’s playground ride known as a merry-go-round can offer a concrete example for understanding the abstract topic of tangential velocity. When riding in the center of the merry-go-round, the ride does not seem to travel very fast, and it may be easy to hang on. On the outer edge of the merry-go-round, however, the ride seems to spin so fast that children cling with all their might to keep from flying off. In actuality, the outer edge must cover the same distance in the same spin as points closer to the center, so it has greater tangential velocity. In other words, it is going faster.