Given an plate that has 2 pins attached to it. Each pin has a single balanced circular disc firmly attached to it. Both of the pins can rotate on their axis in both clockwise and anti clockwise direction. (The setup is similar to a clock).

Now, assume the discs are rotating with the same angular velocity in opposite direction and are same in every possible way. Since, the discs are rotating with the same angular velocity and are same in size, weight etc. there will be no change in center of mass, thus no motion in the plate. The plate itself will be at rest.

Now, suppose we choose 1 point on each disc's circumference (and color them yellow) such that the line joining them is parallel to x-axis. Moreover as both points are travel in +y direction at the instance we chose them (with obviously the same angular velocity, so the line joining them is always parallel to x axis).

The Query is:

Case 1: If we apply a force to the two discs such that, it is applied two points (discussed above). As the points move, the place at which the force is applied also moves with them. The direction of application of force is exactly opposite to the velocity vector at those points, thus, the force is always tangential. Moreover, the force is applied only when the points are travelling in +y direction.

Case 2: The direction and magnitude of force applied remains the same but instead of rotating disk, the force is applied on the platform itself.

Query 1: Would the end angular velocity of the discs differ in the two cases (as in first case the force acts as a deceleration torque on the discs)?

Query 2: Would the end linear velocity of the platform in -y direction differ in two cases? (As in first force is neutralized in decelerating the discs, whereas in second case it acts on the platform directly)?

In the image below blue arrows represent the rough direction of the chosen points (in yellow) along the circumference as the discs rotate and the tangential opposing force at that particular time instance (in red arrows).enter image description here

  • $\begingroup$ The plate moving can't change the disks speed (it can only exert forces on the disks through their axes /pins, which I take are also frictionless), so, yes, the end angular velocity of the disks will differ in the two cases, since in the second there's no braking taking place. $\endgroup$ – stafusa Sep 18 '17 at 11:41
  • $\begingroup$ @sammygerbil Apologies. I will try to update it. The blue arrows show the rough path that the point at which the force applied would take (they were essentially drawn to show opposite rotation). The red arrows are denoting the force (at that particular instance). $\endgroup$ – J.Doe Sep 18 '17 at 13:28
  • $\begingroup$ @stafusa Thank you. I understand. But do I take the linear momentum would be same in both cases no matter where the (same) force is applied on the whole system (any part of disk or any part of platform)? $\endgroup$ – J.Doe Sep 18 '17 at 13:30
  • $\begingroup$ @J.Doe Yes, $\mathbf{F}=d\mathbf{p}/dt$ no matter what. $\endgroup$ – stafusa Sep 18 '17 at 13:36
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    $\begingroup$ @J.Doe, If you want to ask about a specific concept, just choose a simple problem with detail as less as possible. You post in its current form is kind of hard to understand. $\endgroup$ – Mitchell Sep 18 '17 at 14:03