AP Physics Problem

[causearuckus]

A solid sphere is on an incline, mass M and radius R, with a momnet of intertia= (2/5)MR^2. It is released from rest.

I need help finding the minimum coefficient of friction between the sphere and the inclined plane where the sphere will roll down without slipping.

 

[ActuaryTm]

Originally posted by: causearuckus

A: What are things moving at absolute zero?

 

[causearuckus]

Its a mechanics problem.

 

[JonnyStarks]

Free body diagram!
You also have to know the condition for rolling which is escaping me right now (man I only took that 2 months ago)... something to do with the velocity of the centre of mass in relation to the angular velocity/acceleration...

 

[causearuckus]

I have the FBD but i dont know where the moment of inerita comes in

 

[Heisenberg]

I'll give you a hint: The frictional force would have to balance the component of gravity down the ramp at the point where the sphere touches the ramp.

 

[JonnyStarks]

There it is.
Condition for rolling:
acceleration of the centre of mass = angular acceleration of the sphere (1/2R)

So you know the forces acting on it, and Torque=angular accel x I

At least I remember doing a similar problem that way.

 

[Triumph]

Do you know the angle of the incline?

 

[Triumph]

I get mu = 2/7 tan(theta), where theta is the angle of the incline. But I didn't check my work at all, just ran through it once.

The I comes in for your sum of torques. Sum of torques = I alpha. alpha = linear acceleration/radius. That correlates your force summations and torque summations.