Max Angle of Rolling Solid Cylinder on Inclined Plane | CaptFormal

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A block begins to slide on an inclined plane at an angle of 12.95°, indicating that the surface has friction. To determine the maximum angle for a solid cylinder to roll without slipping, the frictional force and torque must be analyzed. The condition for the block to remain at rest involves balancing forces and torques. The discussion focuses on deriving expressions for frictional force and torque on the cylinder. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement


A block of a certain material begins to slide on an inclined plane when the plane is inclined to an angle of 12.95°. If a solid cyclinder is fashioned from the same material, what will be the maximum angle at which it will roll without slipping on the plane?


Homework Equations





The Attempt at a Solution


I really don't know how to even start this problem. Any help will be appreciated. Thanks.

-CaptFormal
 
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Since the block slides when the angle of of inclination θ, the surface is not frictionless.
So what is the expression of frictional force Fr?
If the block remains at rest on the inclined plane, what is the condition?
In the case of cylinder, linear motion of the center of mass must be zero and torque due to Fr should be zero. What is the expression of the torque on a cylinder?
What is the torque on the cylinder due to Fr?
 
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