How Does Roughness Affect the Time Period of a Ball Rolling on a Vertical Hoop?

[Bilbo B]

Homework Statement

Finding the time period dependence upon another factors such as (radius, g, angular displacement) of the ball.

Relevant Equations

torque balance equation

If the ball's rolling on a vertical hoop placed in contact with floor and with the lowest point being the mean position of the ball undergoing to and fro motion with small angular displacement. In what ways it's time period is solved out provided the surface of the hoop is rough.
If the block is in mean position then the total gravitational force is balanced out with the reaction force.
But when it is displaced with small angle, let theta the gravitational force provides torque about the center of hoop and not about the lowest point which is in contact with the ground then such it depends upon the angle. The problem is the reaction force at this point has nothing to do with providing torque and point about which it rotates is the center of hoop.

 

[berkeman]

Homework Statement:: Finding the time period dependence upon another factors such as (radius, g, angular displacement) of the ball.
Relevant Equations:: Using rotational motion mechanism

If the ball's rolling on a vertical hoop placed in contact with floor and with the lowest point being the mean position of the ball undergoing to and fro motion with small angular displacement. In what ways it's time period is solved out provided the surface of the hoop is rough.

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