Calculate the frictional force if the ball is not slipping

AI Thread Summary
To calculate the frictional force on a ball rolling down an inclined plane without slipping, one must consider the torque about the center of gravity, as it simplifies the analysis. The relevant equation involves the frictional force (f), radius (r), and moment of inertia (I), expressed as (f)(r) = I(alpha). For a solid ball, the moment of inertia is I = 2/5mR^2. The calculation focuses on determining the angular acceleration (alpha) under the condition of no slipping. Understanding these principles is crucial for solving the problem effectively.
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Homework Statement



You have a ball rolling down an inclined plane of h height and an angle theta. I have to calculate the frictional force if the ball is not slipping

Homework Equations


t= FRsin theta
I=2/5mR^2

The Attempt at a Solution



Where on the ball is the torque being measure is it the center of gravity or is it at the outer most region of the ball. The ball is solid.
 
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In reality torques (moments) can be sumed about any point, but it will generally be easiest to sum torques about the center of gravity. In this case the only torque present will be that due to friction and will result in the equation of motion of (f)(r)=I(alpha) where f is force friction, r is radius, and I is moment of inertia. From this you just need to solve for alpha when no slipping is present.
 
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