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Sep 7, 2017 at 1:04 comment added JMLCarter 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.
Sep 6, 2017 at 17:57 comment added J.Doe 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.
Sep 6, 2017 at 15:49 comment added JMLCarter Well yes while the force was applied. Sorry I was neglecting friction - but you didn't say so.
Sep 6, 2017 at 12:55 comment added J.Doe 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) ?
Sep 6, 2017 at 12:38 history answered JMLCarter CC BY-SA 3.0