How Does Static Friction Influence Rolling Motion and Torque?

[pacce]

im confused about how to know which direction the static friction points during rolling. if a ball was rolling uphill, its angular deceleration should be caused by a torque, and that torque is from the static friction right? Then wouldn't the static friction be pointing up the hill towards the direction of translation motion, but then does that mean the friction helps to push the ball in translational motion? also in the book, the diagram of a wheel rolling and accelerating to the right has friction in the same direction as acceleration, but the diagram of it rolling downhill has the friction in opposite direction of acceleration, shouldn't the friction always be the force applying the torque for angular acceleration if the only other forces were gravity or a force applied from the center?

 

[Andrew Mason]

im confused about how to know which direction the static friction points during rolling. if a ball was rolling uphill, its angular deceleration should be caused by a torque, and that torque is from the static friction right? Then wouldn't the static friction be pointing up the hill towards the direction of translation motion, but then does that mean the friction helps to push the ball in translational motion? also in the book, the diagram of a wheel rolling and accelerating to the right has friction in the same direction as acceleration, but the diagram of it rolling downhill has the friction in opposite direction of acceleration, shouldn't the friction always be the force applying the torque for angular acceleration if the only other forces were gravity or a force applied from the center?

The static friction on a rolling wheel would be in the direction opposite to the motion of the centre of mass of the wheel. The static friction force does no work since the force is not applied through a distance. It merely acts as a moving fulcrum for the wheel to keep turning. It does not impart any acceleration, angular or linear, to the wheel.

AM

 

[pacce]

but doesn't it apply a torque which causes the angular acceleration (while rolling downhill)

 

[Doc Al]

im confused about how to know which direction the static friction points during rolling. if a ball was rolling uphill, its angular deceleration should be caused by a torque, and that torque is from the static friction right?

Right!

Then wouldn't the static friction be pointing up the hill towards the direction of translation motion, but then does that mean the friction helps to push the ball in translational motion?

Definitely. If a ball that is rolling without slipping with some initial velocity rolls up a hill, it will rise to a higher level than if it just slid up a frictionless hill. The rotational KE ends up giving the ball additional PE.

From a force point of view, the ball has a force mgsinθ acting down the hill and a force due to static friction acting up the hill. The resultant acceleration is less than it would be if there were no friction.

also in the book, the diagram of a wheel rolling and accelerating to the right has friction in the same direction as acceleration,

In the case of the accelerating wheel, presumably there is something giving the wheel a torque about its axle, driving it along. The static friction accelerates the wheel forward, but there is a net torque on the wheel in the opposite direction.

but the diagram of it rolling downhill has the friction in opposite direction of acceleration,

Right. Note that here there is no driving torque applied to the axle, just gravity and friction.

shouldnt the friction always be the force applying the torque for angular acceleration if the only other forces were gravity or a force applied from the center?

If it were just rolling along, with the only forces being gravity or a force at the center (not providing a torque), then yes, the friction must provide the torque (about the center) for any angular acceleration. But that's not the case with the accelerating wheel.

 

[Doc Al]

The static friction on a rolling wheel would be in the direction opposite to the motion of the centre of mass of the wheel.

Not necessarily.

The static friction force does no work since the force is not applied through a distance. It merely acts as a moving fulcrum for the wheel to keep turning.

That's true.

It does not impart any acceleration, angular or linear, to the wheel.

Sure it does. Newton's laws still apply.

 

[Andrew Mason]

Not necessarily.

I was assuming that the body to which the wheels are attached was coasting up the hill. If the wheels are being driven, then the static friction force will be in the direction of motion. Is that what you mean?

Sure it does. Newton's laws still apply.

So, how does a force that does no work transfer energy?

AM

 

[Doc Al]

I was assuming that the body to which the wheels are attached was coasting up the hill. If the wheels are being driven, then the static friction force will be in the direction of motion. Is that what you mean?

That's one example, but stick to the one that started off this thread: A ball rolling up a hill. Which way do you think that static friction acts on the ball?

So, how does a force that does no work transfer energy?

Even though the static friction force does no work--and thus transfers no energy--it still is quite capable of imparting an acceleration. Just like any other force.

 

[Andrew Mason]

That's one example, but stick to the one that started off this thread: A ball rolling up a hill. Which way do you think that static friction acts on the ball?

I am not sure.

If the ball is rolling downhill due to gravity, gravity is applying a downward force on the centre of mass of the ball and this results in a downward torque about the point of contact between the ball and the hill. This means the static friction force is up.

I'll have to think a bit more about the uphill case. If the ball is rolling uphill, gravity is still applying the same downward torque to the ball. But since the ball is rolling in the upward direction and the speed of rotation is slowing, the static friction force should be downward. As I say, I'll have to think a bit more about that.

Even though the static friction force does no work--and thus transfers no energy--it still is quite capable of imparting an acceleration. Just like any other force.

Of course you are right. So long as the force is perpendicular to the direction of motion, no work is done.

But how does it impart an angular acceleration or linear acceleration without doing work?

AM

 

[Doc Al]

I am not sure.

If the ball is rolling downhill due to gravity, gravity is applying a downward force on the centre of mass of the ball and this results in a downward torque about the point of contact between the ball and the hill. This means the static friction force is up.

I'll have to think a bit more about the uphill case. If the ball is rolling uphill, gravity is still applying the same downward torque to the ball. But since the ball is rolling in the upward direction and the speed of rotation is slowing, the static friction force should be downward. As I say, I'll have to think a bit more about that.

Rather than considering torques about the contact point (which is accelerating), consider torques about the center of mass, which is always simpler to interpret. Gravity exerts no torque about the center of mass. Without friction there would be no angular acceleration about the CM.

Of course you are right. So long as the force is perpendicular to the direction of motion, no work is done.

But how does it impart an angular acceleration or linear acceleration without doing work?

I don't understand why you associate a force 'doing work' with its ability to impart an acceleration. From Newton's 2nd law, all forces contribute to the net force which determine's a body's acceleration regardless of whether work is done.

Examples:

Stand still and then start walking. Assuming no slipping occurs, no work is done by static friction yet there is obviously an accelerating force propelling you forward.

Even clearer: Jump into the air. Obviously the ground doesn't move, so it does no real work on you, yet it exerts a force that accelerates you upward.

 

[Andrew Mason]

Rather than considering torques about the contact point (which is accelerating), consider torques about the center of mass, which is always simpler to interpret. Gravity exerts no torque about the center of mass. Without friction there would be no angular acceleration about the CM.

I don't understand why you associate a force 'doing work' with its ability to impart an acceleration. From Newton's 2nd law, all forces contribute to the net force which determine's a body's acceleration regardless of whether work is done.

I am not sure why you don't.

If a force is applied through a distance Δs, work is done in the amount FΔs. So if the body to which the force is applied accelerates, it changes its speed by dv in time dt and it has to move through some distance! It may not be a large distance if the mass is large (eg the earth) but if acceleration occurs, work is done.

Examples:

Stand still and then start walking. Assuming no slipping occurs, no work is done by static friction yet there is obviously an accelerating force propelling you forward.

Interesting point. When I push back on the Earth I accelerate the earth, so the force that my foot applies to the Earth does work. It imparts angular momentum to the earth. I am not sure it is accurate to say that this is the static friction force though.

Static friction allows a force to be applied between my body and the earth. I don't think it accelerates anything. The static friction force is essentially providing an equal and opposite force to whatever force is applied to it. The force that my foot applies to the Earth causes the Earth surface to accelerate in the opposite direction. And the earth, not static friction, applies a force to my body which causes my body to move forward. Static friction just allows my foot and Earth to connect.

AM

 

[Doc Al]

I am not sure why you don't.

If a force is applied through a distance Δs, work is done in the amount FΔs.

So far, so good.

So if the body to which the force is applied accelerates, it changes its speed by dv in time dt and it has to move through some distance!

Not so fast: If a net force acts on a body, Newton's law only says that the center of mass must accelerate. In order for work to have been done, the point of application of the force must move through a distance.

It may not be a large distance if the mass is large (eg the earth) but if acceleration occurs, work is done.

Not necessarily, as the examples in this thread have illustrated.

Interesting point. When I push back on the Earth I accelerate the earth, so the force that my foot applies to the Earth does work. It imparts angular momentum to the earth.

True, but I think we can safely ignore the movement of the Earth during walking for this discussion. We are talking about the work done (or not done) on you as you walk.

I am not sure it is accurate to say that this is the static friction force though.

Why not?

Static friction allows a force to be applied between my body and the earth. I don't think it accelerates anything.

So you think you can just start walking without friction? Try it on slick ice sometime.

The static friction force is essentially providing an equal and opposite force to whatever force is applied to it. The force that my foot applies to the Earth causes the Earth surface to accelerate in the opposite direction. And the earth, not static friction, applies a force to my body which causes my body to move forward. Static friction just allows my foot and Earth to connect.

The horizontal force the Earth applies to your foot is the static friction. No work is done by that force, since there's no displacement at the point of contact. Like any other force, it can and does provide an acceleration.

 

[Andrew Mason]

So far, so good.

Not so fast: If a net force acts on a body, Newton's law only says that the center of mass must accelerate. In order for work to have been done, the point of application of the force must move through a distance.

That is a bit of an over-simplification. Static friction is really a set of tension forces between two interacting bodies at and around the points of contact.

When any macroscopic body collides with (or presses on) any other macroscopic body there are all sorts of tensions created between all the parts of each of the bodies, not just a the points of contact. These tensions combine to impart an acceleration to the centres of mass of both bodies.

Ultimately, it is the sum of all these tensions that results in the (mass x acceleration) of each of the interacting bodies, not just the tension forces at the point of contact. So the resultant (sum) of all these tension forces necessarily ends up doing work.

So you think you can just start walking without friction? Try it on slick ice sometime.

Again, it is not just the static friction between the foot and the earth. It is the tensions within the Earth and the tensions within my body that cause the Earth and my body to push on each other, not just the friction at the points of contact.

The horizontal force the Earth applies to your foot is the static friction. No work is done by that force, since there's no displacement at the point of contact. Like any other force, it can and does provide an acceleration.

Again, I think it is an over-simplication to say that the friction provides that acceleration.

AM