Suppose there is a circular metal disk spinning at a constant angular velocity. Now imagine near to, but not in contact with the first disk, there is an identical metal disk spinning at the same angular velocity but in the opposite direction (ie. W1 = -w2) and the surfaces are parallel to one another. What is the total angular momentum? (ignore friction)
To determine the total angular momentum of the system, we need to consider the angular momentum of each individual disk and then add them together.
The formula for angular momentum is L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Since the disks are identical, their moment of inertia (I) will be the same.
Let's assume the moment of inertia of each disk is represented by I. And since the angular velocity of the second disk is in the opposite direction, it can be represented as -ω.
The angular momentum of the first disk would be L1 = I * ω1
And the angular momentum of the second disk would be L2 = I * (-ω2)
Now, to find the total angular momentum (L_total), we add the angular momenta of both disks:
L_total = L1 + L2
Substituting the values, we have:
L_total = I * ω1 + I * (-ω2)
L_total = I(ω1 - ω2)
The total angular momentum of the system is given by I multiplied by the difference between the angular velocities of the two disks (ω1 - ω2).