Centripetal and average acceleration

[ViewtifulBeau]

This question is all qualitative, but I don't know what centripetal and average acceleration is around a circle. The question is about two runners on a circular track, Runner A on the inside lane, Runner B on the outside lane. The runners have the same SPEED, I think that runner A has a larger centripetal and average acceleration because A has to make a sharper turn. But I think that A and B undergo the same change in velocity as the go around the whole track, even though A will reach the end first. Are my assumptions correct? Thanks

 

[Fermat]

You assumptions are correct, yes.

runner A will have a greater accln because that runner is on a smaller radius, which, in effect, is the same as saying that he makes a sharper turn.

Average accln is the change in velocity divided by the time taken. They both have the same change in velocity, but runner B has taken longer, therefore has a smaller average accln.

If the measurements are taken over one lap though, then they both have the same average accln - it equals zero!

 

[Theoretician]

This question is all qualitative, but I don't know what centripetal and average acceleration is around a circle. The question is about two runners on a circular track, Runner A on the inside lane, Runner B on the outside lane. The runners have the same SPEED, I think that runner A has a larger centripetal and average acceleration because A has to make a sharper turn. But I think that A and B undergo the same change in velocity as the go around the whole track, even though A will reach the end first. Are my assumptions correct? Thanks

If two bodies are traveling around a common centre point and one is 'on the outside track' in relation to the other and they are both traveling at the same speed, the instantaneous centripetal acceleration will be greater for the body on the 'inside track' than the body on the 'outside track'. This can be easily seen because the outer body will lag behind the inner body if each have the same linear speed and so the inner body will have an equal change in velocity in less time than the outer body (or will have a larger change in velocity in the same time).
After one full revolution each, the average acceleration is zero for each body.