### Friday's Physical Law - Going round in circles

~ FPL, Physics*Again in my vain attempt to catch up on my weekly posting due to the myriad issues some of which I mentioned in an earlier post, this post is late, it was due on February 23. *

In an earlier post in this series we touched on the concept of circular motion.

And now then is that other time. For the motion to be circular the velocity must also follow the circle, so at each point there must be a change in velocity at right angles to the motion, this change in velocity is the acceleration that points into the centre of the circle (at right angles to the motion) and is caused by the centripetal force acting on the object.And if this force is always at right angles to the motion then the object will continue at a constant speed the changes in direction will cause it to move in a circle. In this case we call the force a centripetal force, meaning center-seeking, but more about that another time.

So, to have circular motion you can see we need two things, an object travelling at velocity v and a centripetal acceleration a (and hence force F).

To get the motion to be a nice circle you need to have the correct relationship between these two. Obviously (at least I hope so) the size of the circle (to be specific its radius,

*r*) is also going to play a role, in fact the relationship comes out as (after a bit of complicated maths - some of which can be seen here):

*a = v*^{2}/r

*F = mv*^{2}/r

In this case the centripetal force must be the nett force, otherwise the motion would not be circular.

There are many different ways to provide the centripetal force, obvious ones include

- Gravity (for orbits and sloped paths like on a velodrome)
- tension in a piece of string
- Friction (between tyres and the ground)

There is one further issue that people have trouble with when dealing with circular motion and that is the difference between centripetal and centrifugal but that is the subject for another post.

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