What is Circular Motion?
Circular motion describes the movement of an object along a circular path. Even if the object moves at a constant speed (like a car on a circular track), it is still accelerating. This is because its velocity (which is a vector) is constantly changing direction.
This acceleration is directed toward the center of the circle and is known as centripetal acceleration. According to Newton's Second Law, if there is an acceleration, there must be a net force. This inward-pointing force is called centripetal force.
Formulas for Circular Motion
1. Centripetal Acceleration ($a_c$)
Centripetal acceleration is the acceleration required to keep an object moving in a circle. It depends on the object's tangential velocity ($v$) and the radius ($r$) of the circle.
- $a_c$: Centripetal Acceleration (in m/s²)
- $v$: Tangential Velocity (in m/s)
- $r$: Radius of the circle (in m)
As you can see, a higher speed or a tighter turn (smaller radius) requires much more acceleration. This is why you feel "pushed" harder on a tight turn in a car. You can calculate this using our acceleration calculator's principles.
2. Centripetal Force ($F_c$)
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 the centripetal acceleration formula with Newton's Second Law ($F = ma$, which relates to momentum):
- $F_c$: 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)