Centripetal Force - with angular rate

$F_c = "m" * "r" * omega^2$

Enter a value for all fields

The Centripetal Force calculator computes the centripetal force based on the acceleration directed /attachments/a0335317-6066-11e8-abb7-bc764e2038f2/CentripetalForce-illustration.png 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
| $omega$ | - magnitude of the angular 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

Since velocity $"(v)" = omega *r$ , the equation becomes: $F_c = (m • (|omega*r|)^2)/r = m * omega^2 *r$

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 $vec(a_"rad")$ . /attachments/a0335317-6066-11e8-abb7-bc764e2038f2/CentripetalAcceleration-illustration.png Circular Motion

Other Circular Motion Functions

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.
Centripetal Force, CLICK HERE

References

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