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]
However sometimes the period of rotation [math]\displaystyle{ T }[/math], in seconds is given
[math]\displaystyle{ T = \frac{2\pi}{\omega} \,. }[/math]
A Computational Model
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Middling
Difficult
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading
Books, Articles or other print media on this topic
External links
Internet resources on this topic
References
This section contains the the references you used while writing this page