Question

Two disks are rotating about the same axis Disk A has a moment of inertia of 9.99 kg m2 and an angular velocity of 4.51 rad s Disk B is rotating with an angular velocity of 6.35 rad s The two disks are then linked together without the aid of any external torques so that they rotate as a single unit with an angular velocity of 4.24 rad s The axis of rotation for this unit is the same as that for the separate disks What is the moment of inertia of disk B

Answer 1

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 change 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.