Circular Motion - Centripetal Acceleration
Circular Motion - Centripetal Acceleration
\[a_c = \frac{v^2}{r}\]
Variables
ac = centripetal acceleration (m/s²)
v = tangential velocity (m/s)
r = radius of rotation (m)
Description
What is this formula?
This equation calculates the centripetal acceleration required to keep an object moving along a circular path.
When to use it
Use this formula when analyzing circular motion where the tangential velocity and radius are known.
Example
If an object moves at 8 m/s in a circle of radius 2 m:
ac = 8² / 2 = 32 m/s²
Applications
Rotational mechanics, vehicle dynamics, orbital motion, amusement rides, and engineering analysis.
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