Centripetal Acceleration Calculator

What is Centripetal Acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path that is directed toward the center around which the object is moving. It is responsible for changing the direction of velocity vector of the object, thus maintaining its circular motion.

Formula

The formula for centripetal acceleration is:

\[ a = \frac{v^2}{r} \]

Where:

• \(a\) is the centripetal acceleration (m/s²)
• \(v\) is the velocity of the object (m/s)
• \(r\) is the radius of the circular path (m)

Calculation Steps

Let's calculate the centripetal acceleration of an object moving in a circular path with a velocity of 5 m/s and a radius of 2 m:

1. Identify the known values:
   • Velocity (v) = 5 m/s
   • Radius (r) = 2 m
2. Apply the centripetal acceleration formula: \[ a = \frac{v^2}{r} \]
3. Substitute the known values: \[ a = \frac{(5 \text{ m/s})^2}{2 \text{ m}} \]
4. Perform the calculation: \[ a = \frac{25 \text{ m²/s²}}{2 \text{ m}} = 12.5 \text{ m/s²} \]

Example and Visual Representation

Let's visualize the centripetal acceleration with our example:

This visual representation shows:

• The circular path with a radius of 2 m
• The object's velocity of 5 m/s tangent to the circle
• The centripetal acceleration of 12.5 m/s² pointing towards the center of the circle