Monday, 19 March 2007

Friday's Physical Law - Going round in circles

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 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.

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.

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 = v2/r
which with Newton's second law gives us the nett force or the centripetal force:
  • F = mv2/r
Now I used the term nett force above, what I mean by that is the force that is the result of adding all the forces on the object together, for example when we are standing still the nett force on our bodies is zero, but we are experiencing at least two forces, that of gravity pulling down on us and the ground pushing back up (Note: these are not an action/reaction pair). In general when we talk about forces especially in relation to acceleration we are really talking about the nett force.

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
  1. Gravity (for orbits and sloped paths like on a velodrome)
  2. tension in a piece of string
  3. Friction (between tyres and the ground)
Now since the centripetal force is required to keep an object moving in a circle, what happens when we remove that force. Like I said above the centripetal force is the nett force, so if it is removed then there is no force acting on the object and hence no acceleration. So an object released from circular motion will travel in a straight line in the direction of its velocity when released, this can be seen when you think about how one uses a sling to propel projectiles.

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.