Centrifugal Force Calculator

Understanding Centrifugal Force Calculator

Centrifugal force is a pseudo-force observed in rotating reference frames. It acts outward from the axis of rotation.

How to use this calculator

1. Enter the mass of the object in kilograms, \(m\).
2. Enter the angular speed in radians per second, \(\omega\).
3. Enter the radius from the center of rotation in meters, \(r\).
4. Read the centrifugal force in newtons, \(F_{cf}\).

The formula explained

The calculator uses \(F_{cf} = m\omega^2 r\), which gives the centrifugal force for an object in uniform circular motion as seen from the rotating frame. It grows with mass, with the square of angular speed, and with distance from the center.

• \(F_{cf}\) = centrifugal force, in newtons
• m = mass of the object, in kilograms
• \(\omega\) = angular speed, in radians per second
• r = radius or distance from the center of rotation, in meters

Step by step method

1. Start with the formula \(F_{cf} = m\omega^2 r\).
2. Square the angular speed, then multiply by the mass and the radius.
3. Check that \(m\) is in kilograms, \(\omega\) is in radians per second, and \(r\) is in meters.
4. Report the result in newtons, because \(1\) newton is \(1\,\text{kg} \cdot \text{m} / \text{s}^2\).

Worked example

Problem. A \(2.5\) kg object rotates at \(4\) rad/s at a radius of \(3\) m. What is the centrifugal force?

1. Use \(F_{cf} = m\omega^2 r\).
2. Substitute the values: \(F_{cf} = 2.5 \times 4^2 \times 3\).
3. Compute \(4^2 = 16\), so \(F_{cf} = 2.5 \times 16 \times 3 = 120\).

Tips and common mistakes

• Make sure angular speed is in radians per second, not revolutions per minute, unless you convert it first.
• If the radius doubles, the centrifugal force doubles, but if angular speed doubles, the force becomes \(4\) times as large because of the square.

Frequently asked questions