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Consider a rectangular platform in space such that it has 2 vertical rods embedded in its surface equidistant from its geometric center. The platform is parallel to x axis.

Each rod has a balanced circular disc attached to it that is free to rotate parallel to the platform. Assume the discs are rotating parallel to the x axis, one rotating clockwise and another anticlockwise with same angular velocity (w.r.t. the platform). The geometric center of the system is also the center of mass of the system. This system is at rest w.r.t. to an outside observer.

Now, suppose a force is applied to the platform along +x axis for some time period ($t_0$) (from outside, the source of it does not matter). The platform would gain some velocity in +x direction w.r.t. to an outside observer as a result.

Would this acceleration or the outside force also reduce the angular velocity of two discs as compared to the angular velocity earlier (before application of force)?

I think the answer should be yes but I am not sure. Anyone ?

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If the force only creates a translation (is applied at c of m), then no. Angular momentum is conserved.

The angular momentum does not change. The returning half of each disk will be observed to be moving more slowly than the other half, so the apparent centre of rotation in a stationary frame of reference has moved. What is gained in speed (and angular momentum) on one side is compensated for by what is lost in speed (and angular momentum) on the other side.

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  • $\begingroup$ Yes. The force is applied at the CoM. I understand the reasoning. But, from purely engineering perspective the rods which are at the center of axis of the two discs would press towards +x direction along the disc's center in both cases when the platform is accelerating. Wouldn't that create some sort of braking mechanism that would slow the discs down (due to friction during accleration) ? $\endgroup$ – J.Doe Sep 6 '17 at 12:55
  • $\begingroup$ Well yes while the force was applied. Sorry I was neglecting friction - but you didn't say so. $\endgroup$ – JMLCarter Sep 6 '17 at 15:49
  • $\begingroup$ Thank you. Not an issue. Just a followup: Since we know the rods would apply a force that would slow down the disk rotation. Does that (the braking) also provide some sort of an opposing force in the -x axis direction during acceleration that opposes the motion of the platform (i.e. is it possible if the discs were not rotating or rotating at higher/lower angular velocity, the final velocity of the platform for the same force would be greater than the in case they were rotating)? - We are assuming same external force and same time period in both cases. $\endgroup$ – J.Doe Sep 6 '17 at 17:57
  • $\begingroup$ The fact the discs are rotating has no effect on the platform velocity. The mass of the discs (rotating or otherwise) must be accelerated and this requires a force applied to them through the rods. The friction that slows the disc rotation is perpendicular to the direction of motion. I think you are looking at energy and asking "where did the energy that slowed the disks down come from". A rotating disk is itself an energy store, in this scenario as the discs slow that stored energy is being lost as heat via friction. $\endgroup$ – JMLCarter Sep 7 '17 at 1:04

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