Understanding Rolling Without Slipping

[Conservation]

For conditions where an object is rolling without slipping on a rough, flat surface, the object posses a net torque about the center of mass provided by friction at the contact point. Hence, why doesn't the object accelerate radially indefinitely?

For ex, if we had a slippery bowling ball rolling down a rough, flat surface, its radial acceleration would increase until its translational velocity=W*R (no-slip condition met) and then continue to do so. Why does the radial acceleration no longer occur despite the presence of a net torque?

 

[Doc Al]

For conditions where an object is rolling without slipping on a rough, flat surface, the object posses a net torque about the center of mass provided by friction at the contact point. Hence, why doesn't the object accelerate radially indefinitely?

If the surface is horizontal, there would be no static friction and thus no torque. (Ignoring details like rolling resistance.) If it's rolling downhill, then it would keep accelerating.

For ex, if we had a slippery bowling ball rolling down a rough, flat surface, its radial acceleration would increase until its translational velocity=W*R (no-slip condition met) and then continue to do so. Why does the radial acceleration no longer occur despite the presence of a net torque?

Once the "rolling without slipping" condition is met, there is no longer friction acting and no net torque. At least for a horizontal surface.

 

[Conservation]

Why is there friction for a sloped surface and no friction for a flat surface?

 

[Doc Al]

Why is there friction for a sloped surface and no friction for a flat surface?

Friction acts to prevent slipping between surfaces. For a horizontal surface, friction is not need to prevent slipping. Friction is needed for a sloped surface.

 

[Conservation]

I'm sorry, but I don't follow. It's definitely possible to have an object slip or slip/roll on a horizontal surface, and friction is present for those cases...

 

[Doc Al]

I'm sorry, but I don't follow. It's definitely possible to have an object slip or slip/roll on a horizontal surface, and friction is present for those cases...

Only if it's accelerating. Once it meets the no-slip condition, you can change the surface to one that is perfectly frictionless and you won't know the difference. Friction is only needed to change the speed (rotational and translational).

 

[Conservation]

So friction exists before no-slip condition and then becomes 0 once it reaches no-slip? That makes sense logically and satisfies the lack of net torque in rolling without slipping, but I don't see how this is physically possible.

 

[Doc Al]

So friction exists before no-slip condition and then becomes 0 once it reaches no-slip?

Right.

That makes sense logically and satisfies the lack of net torque in rolling without slipping, but I don't see how this is physically possible.

Imagine the surface suddenly became frictionless as the object rolled along. What would be the relative speed of the bottom surface of the object and the frictionless surface? Would there be slipping? (Remember, we are talking about static friction here.)

 

[Conservation]

Relative speed would be 0, which makes the friction static. But shouldn't the static friction still have some form of direction, providing net torque?

 

[Doc Al]

Relative speed would be 0, which makes the friction static.

Since (without friction) there is no slipping (as you said, the relative speed is zero), friction is not needed to prevent it. Only if there would be slipping without the friction, would you need friction.

But shouldn't the static friction still have some form of direction, providing net torque?

The static friction is zero, since it's moving at just the right speed so there is no slipping to prevent.

 

[Conservation]

Okay, I think I understand now for the scenario of the flat surface. Thank you.
What about sloped surface, though? Why would rolling without slipping on a sloped surface have friction?

 

[Doc Al]

Okay, I think I understand now for the scenario of the flat surface. Thank you.

Cool.

What about sloped surface, though? Why would rolling without slipping on a sloped surface have friction?

Since the object is speeding up, the rotational speed must increase accordingly to maintain no slipping. That requires friction exerting a torque.