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In physics problems, I struggle to incorporate the ideas of angular conservation and torque. For example, how do I know when torque is zero in a problem like this:

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can I even apply angular momentum in this problem? I understand that for the most part the angular momentum is conserved and constant when torque is zero.

(side note: a walkthrough of the problem would be helpful.)

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3 Answers 3

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Angular momentum is always conserved for an isolated system, around any arbitrary point you choose. If you have 4 wheels on a car, for example, it won't be convenient to consider the angular momentum of the system because it's better to look just at the angular momentum of each wheel about its axis.

For two planets orbiting the same fixed point, for example, then conservation of angular momentum of the. whole system can be quite useful and convenient to calculate.

For a beam balancing on a pivot with multiple forces acting on it, considering the torque about the pivot point can be a convenient way of telling whether or not it will move.

In this case, the system is the two rollers, the bar, and the engine/device that is keeping each roller spinning at a constant velocity (assumed since they tell you they spin at constant velocity). It looks like the best approach is just to calculate the horizontal force applied by kinetic friction between the wheels and the board.

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  • $\begingroup$ thank you for the explanation. but what about torque? if angular momentum is conserved does that mean torque will be zero? for the question, I assume SHM, is this correct? $\endgroup$
    – thewhale
    Commented Mar 19 at 15:53
  • $\begingroup$ No this is not SHM - SHM involves an object oscillating with a restoring force toward equilibrium. In the same way a force can impart momentum onto an object, torque can impart angular momentum. Torque is not used in this problem because it's not important, though clearly an engine is applying torque to the rollers. $\endgroup$
    – Señor O
    Commented Mar 19 at 16:15
  • $\begingroup$ @SeñorO I don't think you can calculate $N_1$ and $N_2$ without assuming that the torque is zero $\endgroup$
    – Pato Galmarini
    Commented Mar 19 at 16:49
  • $\begingroup$ @PatoGalmarini yes the solution manual also states that torque is zero. i just dont understand why it is $\endgroup$
    – thewhale
    Commented Mar 19 at 17:20
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Assume the total torque is zero, so you can calculate the normal forces and thus the horizontal forces (using zero torque plus zero net vertical force). Then the horizontal force you will get is $F=-\mu Mgx$, where $M$ is the total mass of the bar. That is a harmonic motion, same as if you had a spring with a constant $k=\mu Mg$.

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  • $\begingroup$ this is the one that follows most closely with the solution manual. but how can i arrive to torque is zero without assumption $\endgroup$
    – thewhale
    Commented Mar 19 at 17:22
  • $\begingroup$ Because otherwise the bar will tilt, and you are assuming it is not, like when you have a bar resting on two pillars. The horizontal motion is irrelevant to the vertical one. Assume you start at rest, and then switch the wheels on, the vertical forces should not be affected by the horizontal friction, why would they? $\endgroup$
    – Pato Galmarini
    Commented Mar 19 at 17:24
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A priori, this system does not need to conserve angular momentum because it is not invariant under rotations: gravity has selected a preferred direction (down). (So in the abstraction, gravity is external).

Nor does it need to conserved vertical momentum, since the gravitational potential energy depends on height (which breaks translational invariance in that direction).

If $\mu=0$, it would conserve horizontal momentum, since a translation leaves the problem unchanged.

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