# Homework Help: Circular motion with friction differential equation

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1. Sep 24, 2015

### wololo

1. The problem statement, all variables and given/known data

2. Relevant equations

F=ma
ac=v^2/r
f=uN
v=v0+at
w=v/r
3. The attempt at a solution

v=v0+at
v=vo+umv^2/r
v^2(u/r)-v+vo=0

I don't see what differential equation i could use since the speed is dependent on the friction (equal to friction coeff times centripetal force) which in it's turn is also dependent on the speed

2. Sep 24, 2015

### haruspex

Your v=v0+at equation only applies for constant acceleration. It will not be.

3. Sep 24, 2015

### wololo

As i understand this problem, the centripetal force, which points towards the center of the ring, equals the normal force. In that case, the friction would be equal to a coefficient times the centripetal force. When the speed changes (due to friction), the centripetal force will change (mv^2/r) and so will the normal. However since the speed is dependent on the friction which in turn is dependent on the speed, I seem to be stuck in a circular situation. Would any one have advice to help me find the relation that will allow me to express v? Thanks!

4. Sep 24, 2015

### wololo

my solution gives me v instead of v0 in the denominator. Is there a typo in the statement? Thanks

5. Sep 24, 2015

### TSny

You used the expression v = vo - atant which is not applicable, as haruspex pointed out.

You found atan = μv2/R. Express the acceleration on the left side in terms of the rate of change of the speed.