Does Newton's Third law apply to torque/rotation?

[alkaspeltzar]

You should use the exploded view in your FBDs to avoid confusing yourself:
https://peer.asee.org/the-exploded-...pproach-to-teaching-the-free-body-diagram.pdf

Hey we got there guess that's all that matters now

 

[Shane Kennedy]

Summary:: There are similar 1st and 2nd laws for torques as there are for forces, but it doesn't seem like this applies to N3L?

Propellor driven (drawn?) aircraft with big engines have a tendency to flip over as a result of the "equal and opposite reaction. Pilots have to be careful not to apply too much power until they are traveling fast enough for the ailerons to counteract it.

 

[alkaspeltzar]

Propellor driven (drawn?) aircraft with big engines have a tendency to flip over as a result of the "equal and opposite reaction. Pilots have to be careful not to apply too much power until they are traveling fast enough for the ailerons to counteract it.

True, but its harder to see when there are multiple axis which is why I was trying to think/form the gear example.

But in the end, torque is about a constant axis or point of rotation and I mixing them up. Also if the gears are attached to Earth then it too isn't a closed system so we typically ignore Ang conservation and equal/opposite forces etc as they don't apply

Thanks for good example

 

[Shane Kennedy]

True, but its harder to see when there are multiple axis which is why I was trying to think/form the gear example.

But in the end, torque is about a constant axis or point of rotation and I mixing them up. Also if the gears are attached to Earth then it too isn't a closed system so we typically ignore Ang conservation and equal/opposite forces etc as they don't apply

Thanks for good example

Another example is a planetary gearbox. If just one part is fixed, then the other parts will share the power. In the case of the planets being fixed, the inner and outer will rotate in opposite directions with the opposite (to input direction) torque being experienced by the gearbox mounting

 

[atyy]

Newton's third law is generalized to the conservation of momentum. When Noether's theorem is valid momentum conservation arises from spatial translational invariance, while angular momentum conservation arises from rotational invariance.

The following two excerpts are from Kleppner & Kolenkow (K&K), Introduction to Mechanics, 2nd Ed.

[K&K, Eq 7.7 says torque = rate of change of angular momentum]
"In fact, Eq. (7.7) follows directly from Newton’s second law. Only when we talk about extended systems does angular momentum assume its proper role as a new physical concept."

[K&K, From Section 7.6, p260]
"In Chapter 4 we showed that the translational motion of a system of particles is simple to describe if we distinguish between external forces and internal forces acting on the particles. The internal forces cancel by Newton’s third law, and the momentum changes only because of external forces. This leads to the law of conservation of momentum: the momentum of an isolated system is constant.

In describing rotational motion it is tempting to follow the same procedure by distinguishing between external and internal torques. Unfortunately, there is no way to prove from Newton’s laws that the internal torques add to zero. Nevertheless, it is an experimental fact that internal torques always cancel because the angular momentum of an isolated system has never been observed to change. We shall discuss this more fully in Chapter 8, and for the remainder of this chapter we shall simply assume that only external torques change the angular momentum of a rigid body."

[K&K, Section 8.5, p311]
"The situation shown in figure (a) corresponds to the case of central forces.We conclude that in the particular case of central force motion the conservation of angular momentum follows from Newton’s laws. However, Newton’s laws do not explicitly require forces to be central. We must conclude that Newton’s laws have no direct bearing on whether or not the angular momentum of an isolated system is conserved because these laws do not exclude the situation shown in figure (b). It is possible to take exception to the argument above on the following grounds: although Newton’s laws do not explicitly require forces to be central, they implicitly make this requirement because in their simplest form Newton’s laws deal with particles. Particles are idealized masses that have no size and no structure. In this case, the force between isolated particles must be central, since the only vector defined in a two-particle system is the vector rjk from one particle to the other. ...

Because the spin of an electron defines an additional direction in space, the force between two electrons need not be central. ...

There are other possibilities for non-central forces. Experimentally, the force between two charged particles moving with respect to each other is not central; the velocities define additional axes on which the force depends.

The situation, in brief, is that Newtonian physics is incapable of predicting conservation of angular momentum but no isolated system has yet been encountered experimentally for which the total angular momentum is not conserved. We conclude that conservation of angular momentum is an independent physical law, and until a contradiction is discovered, our physical understanding must be guided by it."

 

[vanhees71]

The conservation of angular momentum, seen from the perspective of Noether's theorems, is not an additional physical law but follows from the isotropy of space. That's why it holds in Newtonian as well as special relativistic physics, because in both spacetime models rotations build a subgroup of the space-time symmetry group (Galilei group and special orthochronous Poincare group, respectively).

 

[atyy]

This is what my physics books says. It says that thru N3L, internal torques on a system should sum to zero. But doesn't say there is a N3L strictly for torque

N3L alone does not mean that internal torques sum to zero.

One needs the additional assumption that all forces are central. Newton's laws (including N3L) plus this additional assumption allows angular momentum conservation to be derived.

See also the quotes from Kleppner & Kolenkow's textbook in post #125.

In addition to K&K, here are additional references that derive angular momentum conservation with the explicit statement of the central force assumption.
http://www.physics.usu.edu/Torre/3550_Fall_2012/Lectures/04.pdf
https://sites.astro.caltech.edu/~golwala/ph106ab/ph106ab_notes.pdf (p37-38, Eq 1.22, 1.23)

 

[vanhees71]

Yes, and the Galilei group thus enforces that you must have all interaction forces between two particles must be central. By definition a closed many-body system obeys all the symmetries and thus all 10 conservation laws resulting from the conserved "Noether quantities" resulting from the 10 independent one-particle subgroups, i.e., energy (homogeneity of time), momentum (homogeneity of space), angular momentum (isotropy of space), and center-of-mass velocity (invariance under Galilei boosts).