How Is Torque Related to Frictional Force?

[PJani]

I am trying to figure out how exactly Angular friction ("torque") is connected with friction force.

Is there any connection between torque friction and force friction?

 

[rock.freak667]

Well torque is related to force by T=rxF

 

[PJani]

Yes i know for that relation but what if i have box on the ground which fully touches ground with all bottom area. Which i spin and i know that static friction is k_s and kinetic is k_k. How can i figure out when box will stop rotating?

Box has some moment of inertia and some mass...

I know that formula is.
$$\omega = 0$$

$$\omega = \omega_0 + \alpha t$$

$$\tau = I \alpha$$

If i toss around elements
$$\frac{(\omega - \omega_0)}{\alpha} = t$$

$$\alpha = \frac{\tau}{I}$$

and if i join equations together
$$\frac{(0 - \omega_0) I}{\tau} = t$$

then what the heck is torque(T)? If i insert $$\tau = r \times F$$ Then i have missing variable r.

 

[rock.freak667]

r would be the distance from the center to where the force is applied.

 

[PJani]

Yes i know, that why i can't get it because box spins on ground and it has full contact on ground whole area is in contact. That why i can't figure out what i could do with r. because r is scalar and not contact area!

 

[rock.freak667]

Yes i know, that why i can't get it because box spins on ground and it has full contact on ground whole area is in contact. That why i can't figure out what i could do with r. because r is scalar and not contact area!

Friction is independent of area and given by F_friction= μN where N is the normal reaction.

 

[PJani]

I can use $$\tau = r \times F$$ for point contacts with ground and then calculate produced torque. Which gives me no problem.

But what if i spin box around ground normal. how can i get then torque which will stop the box from spining on ground?

 

[rock.freak667]

Multiply the frictional force by the distance from the center of rotation.