Centripetal Force and Curving Motion

Created by Chinmay Kulkarni

Main Idea

A centripetal force is a force acting on a body while it has curving motion. In these certain situations, the momentum of the system is not constant, since the direction of motion, or velocity always changes direction while the speed may remain constant.

A Mathematical Model

While an object is in circular motion, the centripetal force is always perpendicular to the velocity and momentum of the object, meaning that the object experiences a force towards the centre of the circle while it is moving. The simple mathematical model for centripetal force is normally [math]\displaystyle{ F_c = ma_c = \frac{m v^2}{r} }[/math] for any object moving in a circle. However in many circumstances, it is helpful to split the centripetal force into parallel and perpendicular forces, or [math]\displaystyle{ F_{para} }[/math] and [math]\displaystyle{ F_{perp} }[/math] respectively. However, since this is circular motion, many times the angular velocity ω in radians/second of the system moving is given.

In this case

[math]\displaystyle{ v = \omega r }[/math]

meaning

[math]\displaystyle{ F_c = {m\omega^2 r} }[/math]

Examples

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