Answer:
Explanation:
Conservation of angular momentum
If both disks have original angular velocity in the same direction, we would expect their final angular velocity to be
4.51 < ω < 6.35
Where 6.35 rad/s would occur if disk B had I = 0
and 4.51 rad/s would occur if disk B had I = ∞
As both disks have a final angular velocity less than their original, One disk must have changed direction of rotation during the collision. Else angular momentum is Not conserved.
If Disk A did not change direction
Disk A had an angular momentum <u>change</u> of
ΔL = I(ωf - ωi) = 9.99(4.24 - 4.51) = -2.6973 kg•m²/s
Disk B changed direction. It first had to reduce its original momentum to zero before spinning back up to its final momentum in the opposite direction. This total momentum change will be equal to that lost by Disk A
I(4.24 - (-6.35)) = 2.6973
I = 2.6973 / 10.59 = 0.254702... ≈ 0.255 kg•m²
If Disk A was the one to change direction
Its change in angular momentum was
ΔL = 9.99(4.51 + 4.24) = 87.4125 kg•m²/s
Disk B had to lose the same amount of angular momentum during the collision
87.4125 = I(6.35 - 4.24)
I = 41.42772 ≈ 41.4 kg•m²
I leave it to you to determine which is correct as we cannot tell from the information given in the question.
