Centripetal Force Calculator

How to Calculate Centripetal Force

Centripetal force is the force that acts on a body moving in a circular path, directed toward the center around which the body is moving. Understanding how to calculate this force is crucial in various applications, from engineering to physics.

What is the Formula for Centripetal Force?

The formula for centripetal force is:

\[ F = \frac{mv^2}{r} \]

Where:

• \(F\) is the centripetal force (in Newtons, N)
• \(m\) is the mass of the object (in kilograms, kg)
• \(v\) is the velocity of the object (in meters per second, m/s)
• \(r\) is the radius of the circular path (in meters, m)

Alternatively, if using angular velocity (\(\omega\)), the formula is:

\[ F = m\omega^2r \]

What are the calculation steps?

1. Identify the mass of the object (\(m\)).
2. Determine the velocity (\(v\)) or angular velocity (\(\omega\)) of the object's circular motion.
3. Measure the radius (\(r\)) of the circular path.
4. Apply the appropriate formula: \(F = \frac{mv^2}{r}\) or \(F = m\omega^2r\).

Example of Centripetal Force Calculation

Let's calculate the centripetal force on a 0.5 kg object rotating in a circle with a radius of 2 meters at a velocity of 6 m/s:

Given:

• Mass (\(m\)) = 0.5 kg
• Velocity (\(v\)) = 6 m/s
• Radius (\(r\)) = 2 m

Using the centripetal force formula:

\[ F = \frac{mv^2}{r} \]

\[ F = \frac{0.5 \times (6)^2}{2} \]

\[ F = \frac{0.5 \times 36}{2} \]

\[ F = 9 \text{ N} \]

Therefore, the centripetal force acting on the object is 9 Newtons.

Diagram of Centripetal Force

The following diagram illustrates the concept of centripetal force:

This diagram shows an object (blue circle) moving in a circular path. The black dashed line represents the radius (r), the green arc represents the velocity (v), and the red arrow shows the direction of the centripetal force (F) acting on the object, which is always directed towards the center of the circle.