Suppose I have a circular metal disk spinning at a constant angular velocity. Now imagine near to, but not in contact with the first disk, I have 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 find the total angular momentum of the system, we need to consider the angular momentum of each disk and add them together.

The angular momentum (L) of an object is given by the product of its moment of inertia (I) and its angular velocity (ω). The moment of inertia depends on the mass distribution and shape of the object.

For a circular disk spinning about its central axis, the moment of inertia can be calculated using the formula I = 0.5 * m * r^2, where m is the mass of the disk and r is its radius.

In this case, both disks are identical, so they have the same moment of inertia (I) and angular velocity (ω). Let's assume the mass of each disk is m and the radius is r.

The angular momentum of each disk can be calculated as L = I * ω = (0.5 * m * r^2) * ω.

Since the two disks are spinning in opposite directions, the angular velocities have opposite signs. So, the angular momentum of the first disk will be L1 = (0.5 * m * r^2) * ω and the angular momentum of the second disk will be L2 = (0.5 * m * r^2) * (-ω).

To find the total angular momentum, we add the individual angular momenta together: L_total = L1 + L2 = (0.5 * m * r^2) * ω + (0.5 * m * r^2) * (-ω).

Simplifying this expression, we get: L_total = 0.

The total angular momentum of the system is zero. This is because the two disks have equal and opposite angular momenta, canceling each other out.