Rotational mechanics

Urmi Roy

This is applicable in the case of,say for example a box being dragged accross the floor, where friction plays a plain role of opposing relative motion between the box and the floor--here, it's converting mechanical energy into heat energy and hence dissipating it. In this case, friction does its expected role of preventing motion.

However, in case of rolling,it is seen that the friction is responsible for acceleration of the wheel,so it's not dissipating energy in this case,instead, it's speeding the wheel up,which kind of appears as if its 'providing' energy to the wheel.

This is where I'm having the problem.

Well, I'm a little confused if we can consider the initial linear momentum being conserved by having the final sum of angular and linear momentum equal to it..can we sum angular and linear momenta?

vin300

I didn't mean centre of mass changes position within the body, it changes position in the observer's frame.
Whatever internal changes take place in the body, its CM does not change position in the observer's frame but changes in its own frame, so the observer interprets "no linear motion"

vin300

Exactly, the friction must be opposite to the velocity, that is the velocity of the body at the point of contact, and not the velocity of its CM.
Whatever the motion, friction is always "resistive".



It is towards the right.
Isn't that stupidity by a proffessor in a technical institute?It forms a curve of contact.

BobbyBear

Urmi, I think the inconsistency lies in the assumption that the friction force is to the left. As DocAl has explained in this thread, you deduce the friction force that is compatible with Newton's laws. If there is no external force or torque upon the wheel prompting its movement, and the wheel is rolling and not slipping, then the friction force must be zero. This is the only compatible solution to applying both Newton's law of linear and rotational motion to the wheel in which you must consider the friction force as an unknown to be solved for (although under the assumption that static friction is capable of preventing slipping even if in the end the friction force is zero). The wheel will carry on its motion with uniform angular velocity indefinitely: it will neither accelerate nor deccelerate.

Although it seems a little strange to think that the friction force in this case is zero, remember that this is what the rigid-body model is predicting. And as the author of your book explained, it's not what exactly really happens, as we know by experience the wheel would tend to slow down if there was no external force (or torque) in favour of provoking its movement. But under the ideal assumptions this is what would happen, and what approximately happens when the two surfaces are almost indeformable.

BobbyBear

You'd sum up the kinetic energies of translation and rotation.

BobbyBear

friction is indeed in the direction opposing the relative velocity at the point of conctact, though if I may add, in the case of static friction, the relative velocity at the point of contact is nil, so the direction of the friction force is such that it opposes the impending relative velocity, if you get me (ie. the relative velocity that would be if the surfaces were frictionless).

vin300

Rigid bodies rolling without slipping might not dissipate mechanical energy as heat, the forces acting may weaken its intermolecular forces which break down at a later point of time. The energy is conserved.

vin300

When the body comes in contact with the surface in a direction different from the normal reaction or weight, it exerts a force on the suface and the surface exerts an equal force on the body but this force does not in any way assist the motion of the body, so it loses energy.

BobbyBear

Urminess,

adding to what I said in reference to the paradoxical scenario from the extract of your book about the friction force having to be zero, the fact that the friction force is zero doesn't mean that there could be a nonzero static friction force if so required (eg if another external force were to come into play). That is, the maximum static friction force is greater than zero. In this case, the friction force is zero, but the wheel is rolling without slipping, thus the linear velocity of the centre of mass is related to the angular velocity of the wheel.

But if the maximum friction force was zero, then even though we'd have exactly the same forces acting upon the wheel, and the wheel would be rotating with the same constant angular velocity (which would be whichever intial angular velocity you like), the wheel would be slipping without rolling (or rolling and slipping, depending on the initial movement - but in any case the rolling would not be due to the friction and the two movements would be uncorrelated), and the linear velocity of its centre of mass would be constant but arbitrary.

How would the system "know" whether there is a capacity for friction or not, if in both cases the friction force (by requirement of the conservation laws) is nil? Well you could think how the system would respond if you were to apply an inifinitesimal force to the wheel - in the first case, a nonzero friction force would appear, so that the movement provoked by this infinitesimal force would be a rolling without slipping movement, but not so in the second case, as that infinitesimal force would contribute to the system's linear movement but not affect its rotational movement. Since the case we've described is an ideal limiting case, in reality the system would never be faced with this quandary, as it would always be somewhat away from the ideal case, and it would know in which situation it stands.

BobbyBear

o:
This crushes all my notions:( Please explain? And, please tell me if you're considering there to be "rolling friction", maybe we're just thinking of different things? I'm assuming there is no "rolling friction", because the contact surfaces are not deforming, and contact occurs at a single point . . . although as I've discussed earlier, one could consider 'rolling friction' (for the sake of approximating reality better) as well as the bodies to be perfectly rigid (for the sake of applying Newton's laws using concentrated forces instead of having to consider internal stresses and what not), in which case I agree that there'd be energy dissipated as heat even though the wheel is not slipping, but due only to the 'rolling friction' which is really an attempt to quantify the energy that goes into deforming the surfaces.

Doc Al

OK, this is just a description of rolling friction. The deformable surface is "bunched up" a bit ahead of the rolling sphere, which changes the direction of the force it exerts on the sphere.

I'm not familiar with that one.

Neglecting rolling friction, there are no friction forces acting on the rolling sphere. It would just keep rolling.

vin300

Before I could edit it understanding the mistake, it said I've to login again and the statement remained.
The contact surface must break apart after some time if the friction is too much as I said earlier.

Doc Al

Quote by Doc Al Static friction acting on the wheel does no work--the displacement of the point of contact is zero. However, Newton's laws still apply and that force does contribute to the wheel's acceleration. But don't confuse that with doing work--the ground is not an energy source.

As long as we are just talking about static friction (and ignoring rolling friction due to deformation of the surface), there is no relative motion between the contact point and the surface. No slipping means no displacement and thus no work being done. Work is done by kinetic friction (and rolling friction), not by static friction. This is why you can apply conservation of mechanical energy to the wheel rolling down the incline--there are no dissipative forces (the friction is static).

When the wheel rolls down the incline without slipping, static friction acts up the incline. That friction does two things:
(1) It slows down the translational motion of the wheel. (The net force on the wheel down the incline is less than it would be on a frictionless surface, thus the wheel's acceleration is less.)
(2) It increases the rotational speed of the wheel, since it applies a torque.

The friction doesn't provide energy, it just allows some of the gravitational energy to be converted to rotational kinetic energy.

Another example: When you walk or run (without slipping), again friction propels you forward yet it does no work and provides no energy. The energy is provided by your muscles; ground friction allows you to convert your internal chemical energy into translational kinetic energy. (If friction provided the energy, you wouldn't get tired. )

BobbyBear

O: if the friction is static, how would there be kinetic friction as well? There either is relative motion or not..

BobbyBear

ooh, I think you just mean in general . . .
obviously the friction cannot be static and kinetic at the same time:P Sorry, I misinterpreted your meaning

BobbyBear

Ya, I agree, friction cannot, by its very nature, increase the overall motion of an object, though ideally, if there is only static friction (and no deformation), there would be no dissipation of energy either. By definition static friction cannot do work! (another issue is whether in reality you'd have whatever other dissipating phenomena taking place).

Doc Al

That's true. At any given time there's either static or kinetic friction, not both. I was just pointing out that work is done by kinetic friction, not static friction.