Enter the total change in position, radius, and time into the calculator to determine the centripetal velocity.

Centripetal Velocity Formula

The following equation is used to calculate the Centripetal Velocity.

Vc = D/(r*t)
  • Where Vc is the centripetal velocity (rad/s)
  • D is the distance traveled (m)
  • r is the radius (m)
  • t is the time (s)

To calculate the centripetal velocity, divide the distance by the product of the radius and time.

What is a Centripetal Velocity?

Definition:

A centripetal velocity is a measure of the angular velocity of an object relative to the radius of rotation.

How to Calculate Centripetal Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Centripetal Velocity.

First, determine the distance traveled. In this example, the distance traveled is found to be 30m.

Next, determine the radius. For this problem, the radius is found to be 10m.

Next, determine the time. In this case, the time is measured to be 6 seconds.

Finally, calculate the Centripetal Velocity using the formula above:

Vc = D/(r*t)

Vc = 30/(6*10)

Vc = .50 rad/s

FAQ

What is the difference between centripetal velocity and tangential velocity?

Centripetal velocity refers to the rate at which an object moves towards the center of a circular path, maintaining the object’s circular motion. It is often measured in radians per second (rad/s). On the other hand, tangential velocity is the linear velocity of an object moving along the circular path, measured at any point tangent to the circle. It represents how fast the object is moving along the circle, rather than towards the center.

Why is the radius important in calculating centripetal velocity?

The radius of the circular path is crucial in calculating centripetal velocity because it directly influences the velocity’s magnitude. A larger radius means that for a given distance and time, the centripetal velocity will be lower, as the object has more space to complete its circular path. Conversely, a smaller radius results in a higher centripetal velocity, indicating a tighter turn at a faster rate.

Can centripetal velocity change, and what factors affect it?

Yes, centripetal velocity can change. It is affected by three main factors: the distance traveled by the object, the radius of the circular path, and the time taken to travel that distance. Any change in these factors will result in a change in centripetal velocity. For example, increasing the distance while keeping the radius and time constant will increase the velocity, as will decreasing the time or radius.