Moment of Inertia of a Rotating Disk

[Student149]

Homework Statement

Given a non magnetic rectangular plate with dimensions: L & B. The plate is of uniform density and thickness.There are 2 points equidistant from the center of the rectangular plate along the line at B/2. Both of these pivot points have 2 disks of radius R and mass M that are freely able to rotate on each point parallel to the plane. Each disk is uniformly thin and perfectly balanced. The disks are parallel to each other.

Each disk is non magnetic other than one small part that is metallic along the edge (shaped in the form of a subsection of a ring, the exact size does not matter). The purpose of them is to use them for braking. There are two electromagnetic brakes located near the outer side of each disk (left and right) located on the plate line at B/2.

The left disk rotates (on a plane parallel to the rectangular plate) in clockwise direction and another in the anticlockwise direction with uniform angular velocity (a₀ degrees/second). Thus, the center of mass of the plate does not move.

When the brakes are charged (at appropriate time), they provide the electromagnetic braking (by pulling at the magnetic part of the disk when it passes near them).

Query 1: What is the direction of the net force the system (plate and disks) experiences when the brakes are applied?
Query 2: How is the magnitude of this force relating to:

1. Mass of disks.
2. Their angular velocity.

Query 3: What would be the answer to above two if the plate's upper and lower half have uniform density but the upper half of the plate has twice the density as the lower half of the plate.

Homework Equations

The Attempt at a Solution

Ans 1: I think the direction of net force experienced by the system should be upwards.
Ans 2: Not sure about this one.
Ans 3: Not sure about this one either.

 

[Student149]

A rough sketch of the setup.