What is the relationship between torque, linear force, and rolling resistance?

[aspodkfpo]

Homework Statement

Is the rolling resistance when something is moving the same as the maximum rolling resistance for when it is still?

Relevant Equations

n/a

Say that I have a round object on a table and it is still. If I apply a force and it doesn't move the resistive force is rolling resistance rather than a frictional force right?

Now I must be able to apply forces in different amounts until it exceeds a boundary for the object to move similar to static frictional force, right?
I would assume that this boundary point is the rolling resistance as something moves, as every new point on the circle is essentially a new stationary point?

 

[Halc]

If I put a large spherical rock in the middle of a dirt playing field, it takes considerable force to move it.

If it starts moving by sliding, then it is static frictional force first being overcome. If it begins to move by rolling, then it is rolling resistance that is first overcome.

Much might depend on how/where the force is applied to the object. If I apply a linear force low enough, static friction will be overcome first, and it might actually begin to roll backwards, as illustrated by 'english' being put on a billiard ball. If I apply only torque and enough of it to exceed the static resistance, it will begin to slide backwards with forward rolling, illustrated by a car peeling out.

 

[berkeman]

Homework Statement:: Is the rolling resistance when something is moving the same as the maximum rolling resistance for when it is still?
Relevant Equations:: n/a

Say that I have a round object on a table and it is still. If I apply a force and it doesn't move the resistive force is rolling resistance rather than a frictional force right?

Now I must be able to apply forces in different amounts until it exceeds a boundary for the object to move similar to static frictional force, right?
I would assume that this boundary point is the rolling resistance as something moves, as every new point on the circle is essentially a new stationary point?

"Rolling Resistance" for most wheels and tires is a combination of bearing friction and tire (and ground) deformation.

https://en.wikipedia.org/wiki/Rolling_resistance

 

[jbriggs444]

Now I must be able to apply forces in different amounts until it exceeds a boundary for the object to move similar to static frictional force, right?

It depends.

I rather like the example of a spherical boulder in the middle of a field. That spherical boulder sits in a little divot. It made that divot by the action of its own weight making a shallow impression in the soil.

In order to roll the boulder, you have to roll it up over the lip of its divot hole. That requires some torque. That torque is "rolling resistance".

Now the question arises -- if you get the boulder rolling at speed, will it have time to keep extending its depression into a trench at that same depth as the starting divot? Or will it be rolling in a trench with a depth that depends on rolling speed?

 

[haruspex]

Another complication is if it is not perfectly round. If it is resting on a bit of a flat then it will take some extra force to get it going, but once it has sufficient momentum you only need to supply enough force/work to meet the average need over a revolution.
Note that, conversely, it could be resting on a slightly high point, so rolling resistance could increase.

 

[aspodkfpo]

If I put a large spherical rock in the middle of a dirt playing field, it takes considerable force to move it.

If it starts moving by sliding, then it is static frictional force first being overcome. If it begins to move by rolling, then it is rolling resistance that is first overcome.

Much might depend on how/where the force is applied to the object. If I apply a linear force low enough, static friction will be overcome first, and it might actually begin to roll backwards, as illustrated by 'english' being put on a billiard ball. If I apply only torque and enough of it to exceed the static resistance, it will begin to slide backwards with forward rolling, illustrated by a car peeling out.

Does torque and a linear force not have the same effect?

 

[haruspex]

Does torque and a linear force not have the same effect?

Depends what you mean by applying a torque. To exert a pure torque, i.e. no net linear force, the natural way is to exert two equal and opposite forces and on different lines of action.
This will not be exactly the same as applying any single linear force.

 

[aspodkfpo]

Depends what you mean by applying a torque. To exert a pure torque, i.e. no net linear force, the natural way is to exert two equal and opposite forces and on different lines of action.
This will not be exactly the same as applying any single linear force.

What exactly is the difference? With the single linear force there is compression of the circle and with torque it just rotates about the spot?

 

[haruspex]

What exactly is the difference? With the single linear force there is compression of the circle and with torque it just rotates about the spot?

You only show the two forces exerting the torque. Yes, it will rotate, accelerating, on the spot... assuming they are equally spaced from the mass centre.
If you take one away the rotational acceleration will halve, but there will also be a linear acceleration.
Did you intend other forces present?

 

[aspodkfpo]

You only show the two forces exerting the torque. Yes, it will rotate, accelerating, on the spot... assuming they are equally spaced from the mass centre.
If you take one away the rotational acceleration will halve, but there will also be a linear acceleration.
Did you intend other forces present?

gravity and normal force. was wondering how torque and linear force differs, that's why I provided my explanation.

 

[haruspex]

gravity and normal force.

And friction?

 

[aspodkfpo]

And friction?

Yes.

 

[haruspex]

Yes.

If you apply a pure torque to a wheel standing on a frictional surface then, up to the static friction limit, you may achieve just the same as with a single force. So in some circumstances it is equivalent in effect, but not in others.

 

[Halc]

Does torque and a linear force not have the same effect?

Imagine a pickup truck sitting on a frictionless surface, carrying a cannon.

Torque is the guy hitting the gas. The wheels all spin but the truck goes nowhere.

Linear force is firing the gun. The truck now moves but the wheels do not spin.

Put in friction, and the one motion blends with the other, and there is no big difference except perhaps heat loss if some of the friction is not static. Similar results from identical energy input.