Rolling motion with slipping

[Just a nobody]

This isn't actually a homework question, but the style of it fits best in this forum.

Diagram
http://img355.imageshack.us/img355/9836/text5029jb0.png

• $$\tau$$ - torque of wheel
• $$R$$ - radius of wheel
• $$f_k$$ - force due to kinetic friction

Question
Is the translational acceleration of the wheel independent of the torque when the wheel is slipping? That is, if the torque is increased, will $$f_k$$ increase?

My attempt (Not necessarily correct)

Additional variables:

• $$u_k$$ - coefficient of kinetic friction between floor and wheel
• $$N$$ - normal force
• $$m$$ - mass of wheel
• $$g$$ - acceleration due to gravity

$$N = mg$$ (since it's on a flat surface)
$$f_k = u_k N = u_k m g$$

$$\tau$$ does not appear in the equation, so $$f_k$$ is independent of torque. No matter how much the torque is increased, $$f_k$$ will not increase if the wheel slips.

Thanks for reading through my question,
David

 

[Dick]

Well, sure. If the frictional force is purely due to kinetic friction, it's only dependent on the normal force and independent of torque.

 

[Just a nobody]

Okay, thank you very much for answering. My intuition told me otherwise, so I wanted to verify my answer.

 

[Dick]

Your intuition probably told you otherwise because if the wheel is not slipping then you are dealing with static friction which is very dependent on the applied force. Even if it is slipping kinetic friction is only an approximate model. Don't dis your intuition too much.