Centripetal Force Calculator

What is Centripetal Force?

Centripetal force is a force that acts on a body moving in a circular path and is directed toward the center around which the body is moving. This force is necessary for circular motion as it constantly changes the direction of the body's velocity, keeping it in a circular path.

Formula

The formula for centripetal force is:

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

Where:

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

Calculation Steps

Let's calculate the centripetal force acting on a 0.5 kg object moving in a circular path with a radius of 2 meters at a speed of 3 m/s:

1. Identify the known values:
   • Mass (m) = 0.5 kg
   • Velocity (v) = 3 m/s
   • Radius (r) = 2 m
2. Apply the centripetal force formula: \[ F = \frac{mv^2}{r} \]
3. Substitute the known values: \[ F = \frac{0.5 \text{ kg} \times (3 \text{ m/s})^2}{2 \text{ m}} \]
4. Perform the calculation: \[ F = \frac{0.5 \times 9}{2} = 2.25 \text{ N} \]

Example and Visual Representation

Let's visualize the centripetal force with our example:

This visual representation shows:

• The circular path with a radius of 2 m
• The object's velocity of 3 m/s tangent to the circle
• The centripetal force of 2.25 N pointing towards the center of the circle