B Static friction needed for rolling without slipping

AI Thread Summary
A wheel rolling down an inclined plane without slipping has a contact point with zero velocity due to the cancellation of its rotational and translational components. The forces acting on the wheel include static friction and the parallel component of weight, with static friction being the only force that can exert torque. Adequate static friction is necessary to ensure that the acceleration of rotation matches the acceleration of linear motion; insufficient friction leads to slipping. Without static friction, the wheel would slide down the incline without rotating, while inadequate friction results in rotation due to kinetic friction that does not match linear motion. The discussion emphasizes the critical role of static friction in maintaining rolling motion without slipping.
adjurovich
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If we had a wheel rolling without slipping down the inclined plane, kinematically its velocity would be 0 at the contact point to the ground since the rotational and translational components of velocity would cancel out.

Speaking of forces, forces acting on body would be static friction and the component of weight parallel to the inclined plane. The only force that will exert torque will be static friction since it’s tangential. Now, speaking theoretically, should the adequate static friction for such motion be the static friction that is able to “reduce” component of weight force and cause rotation, but so that acceleration of rotation = acceleration of linear motion?

I tend to conclude that if force of friction wasn’t strong enough, it would decrease net linear force, but also exert torque that can’t provide enough tangential acceleration so tangential acceleration would be smaller than linear and slipping would occur.

Are my statements wrong?
 
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adjurovich said:
acceleration of rotation = acceleration of linear motion
acceleration of rotation * radius = acceleration of linear motion

adjurovich said:
if force of friction wasn’t strong enough ... slipping would occur.
Yes. For example, in the limit without friction it would just slide down without rotating.
 
A.T. said:
Yes. For example, in the limit without friction it would just slide down without rotating.
Just to make things clear, did you mean when there is no static friction? Obviously there would be no net torque and body would just slide down without rotating.
 
adjurovich said:
Just to make things clear, did you mean when there is no static friction? Obviously there would be no net torque and body would just slide down without rotating.
Yes. And if static friction is insufficient it will slide and rotate due to kinetic friction, but to slow to match the linear motion.
 
A.T. said:
Yes. And if static friction is insufficient it will slide and rotate due to kinetic friction, but to slow to match the linear motion.
Thanks for help!
 

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