Circular motion with friction differential equation

[wololo]

Homework Statement

Homework Equations

F=ma
ac=v^2/r
f=uN
v=v0+at
w=v/r

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

 

[haruspex]

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

 

[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 anyone have advice to help me find the relation that will allow me to express v? Thanks!

 

[wololo]

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

 

[TSny]

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

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