Centripetal Force

The Centripetal Force calculator computes the centripetal force based on the acceleration directed toward the center of a circular motion with constant angular velocity and the mass of the object.

INSTRUCTION: Choose units and enter the following:

• (r) - radius of the constant circular motion
• |v| - magnitude of the tangential velocity
• (m) - mass of the object.

Centripetal Force (F_c): The calculator computes the resulting Centripetal Force (F_c) in Newtons.  However, the user can automatically convert this to other force units via the pull-down menu.

The Math / Science

The formula for centripetal force is:

`F_c = (m • |v|^2)/r`

where:

• F_c is the centripetal force
• m is the mass of the object
• v is the velocity of the object
• r is the radius of the circular motion

Note than if a mass is moving in this circular motion and is affected by this acceleration due to changing angular velocity, that mass will feel a force along the vector direction of `vec(a_"rad")`. Circular Motion 

Circular Motion Calculators

• Centripetal Force
• Centrifugal Force
• Angular Frequency as a function of orbital period,.
• Speed of Circular Motion as a function of orbital period and radius, CLICK HERE.
• Radial Acceleration as a function of orbital period and radius, CLICK HERE.
• Acceleration in non-uniform Circular Motion, CLICK HERE.

References

• Light and Matter(Dr. Benjamin Crowell) Chapter 9.2  Uniform circular motion