- #1
Vriska
- 138
- 2
Homework Statement
I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving.
Homework Equations
I = 2/5 MR^2
torque = I*alpha = R x F
The Attempt at a Solution
[/B]before anything, I don't get why there's a minimum friction even happening, there a torque and there's nothing to counter that, why wouldn't it roll huh?
So sphere's there, exerting a normal force of mgcos (o) where o is the angle of incline.
the friction results in torque around centre of mass
u(coeff of friction) * mg cos (o) * R = I * Alpha
u mg cos(o) = 2/5 ma - (i)
soo we need we need mg sin (o) - u mgcos(o) =ma = 5/2 u mg cos(o)
u = 2/7 tan(o) or something
but I don't get it,I don't get what I've done. if it had a greater or lesser coefficient of friction would it what - roll slower, roll faster? (i) seems to be suggesting that. That doesn't seem to make sense to me :/