Question

Two concentric rings are each free to rotate about an axis through their center. The outer ring has mass 1 kg and radius 2 m, the inner one mass 2 kg and radius 1 m. The outer ring is at rest while the inner ring rotates with a speed of 1 revolution per second. An internal mechanism connecting the two axes flips the axis of the inner ring (by 180 degrees). The axis of the outer ring is fixed to the earth. What is the speed of the outer ring after the flip?

Answer 1

i suspect, but do not know, that this question wants you to consider conservation of angular momentum: \(I_1 \omega_1 = I_1 \omega_1^* + I_2 \omega_2\) where \(\omega_1^* = -\omega_1\)

however, the mechanism described in the question makes no sense to me in that i do not see the reason why momentum needs to be conserved between 2 unconnected bodies as they are described here.....

Answer 2

So one of them is spinning in the opposite direction?

Answer 3

I set L1 = L2. where one side of the equation is .5 rev/s

Answer 4

if you flip the inner ring, its angular momentum vector flips 180deg also.

and if you were to look down at the inner ring from above, you would see the +2π rads/s change to -2π rad/s

that change in angular momentum requires a torque from somewhere within the system/ setup, and i suspect the point of the question - though it is vaguely worded IMHO - is that the equal and opposite torque experienced by the outer ring causes it to start spinning.

hence
\[I_1 \omega_1 = I_1 \omega_1^* + I_2 \omega_2\]
\[\omega_1^* = -\omega_1\]