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Old Sep 17th 2017, 07:02 AM   #1
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Deceleration force in Newtonian Mechanics

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.

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, the force is only applied on the two points (discussed above) such that as the points move point at which the force is applied also moves along with them. The direction of application of force is exactly opposite to the velocity vector at those points. Thus, the force is 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 CoM 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).

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Old Sep 20th 2017, 06:24 AM   #2
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In both cases the angular momentum of the system remains unchanged - it was zero to start with and is zero afterwards. And in both cases the linear momentum of the system goes from zero to some value dependent on the magnitude and duration of the forces applied. You seem to think that in case 1 the application of the force only causes the discs to stop rotating, but actually the forces also cause the system to start moving in the -y direction.
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deceleration, force, mechanics, newtonian

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