What is Centripetal Force?
Circular motion describes the movement of an object along a circular path. Even if the object moves at a constant speed, it is still accelerating because its velocity (a vector) is constantly changing direction.
This inward-pointing acceleration is called centripetal acceleration ($a_c$). According to Newton's Second Law ($F=ma$), if there is an acceleration, there must be a net force. The centripetal force ($F_c$) is the name given to this net force that points toward the center of the circle, causing the object to follow a curved path.
The Centripetal Force Formula
Centripetal force is not a new *type* of force. It is the label we give to the net force that *causes* the centripetal acceleration. This force can be provided by:
- Tension (e.g., swinging a ball on a string)
- Gravity (e.g., the Moon orbiting the Earth)
- Friction (e.g., a car turning on a road)
- Normal Force (e.g., a roller coaster in a loop)
It is calculated by combining Newton's Second Law ($F = ma$) with the formula for centripetal acceleration ($a_c = v^2 / r$). This relationship is fundamental to understanding momentum and acceleration in a circular path.
- $F_c$: Centripetal Force (in Newtons, N)
- $m$: Mass of the object (in kg)
- $v$: Tangential Velocity (in m/s)
- $r$: Radius of the circle (in m)
As the formula shows, the force required increases with the square of the velocity ($v^2$). This means doubling your speed on a turn requires *four times* the centripetal force (e.g., friction from your tires) to hold the turn.