To determine the tangential speed in circular motion, you can use the formula:

where:

• $v$ represents the tangential speed,
• $r$ denotes the radius of the circular path, and
• $\omega$ is the angular velocity.

In circular motion, an object travels along a circular path at a constant speed. The tangential speed refers to the speed of the object along the tangent to the circle at any specific point. This speed is always perpendicular to the radial direction, which points toward the center of the circle.

The tangential speed can be computed using the formula:

where:

• $v$ is the tangential speed,
• $r$ is the radius of the circle, and
• $\omega$ is the angular velocity, defined as the rate of rotation around the center of the circle, typically measured in radians per second.

For instance, consider a car moving along a circular path with a radius of $10$ meters and an angular velocity of $2$ radians per second. The tangential speed can be calculated as follows:

Substituting the values, we have:

Thus, the tangential speed of the car is $20$ meters per second.