Question

Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.7 kg · m2 and an angular velocity of +7.7 rad/s. Disk B is rotating with an angular velocity of -10.4 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 -2.5 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

Angular momentum = I?

I₁ = Moment of inertia of disk A = 3.7 kg.m^2

?₁= angular velocity of disk A = 7.7 rad/s

Angular momentum of disk A = (3.7)(7.7)=28.49

I₂= momentof inertia of disk B

?₂ = angular velocity of disk B=(-10.4) rad/second\

?= angular velocity of disk A and disk B combined= -2.5rad/s

Using the consrvation of angular momentum

I₁?₁ + I₂?₂ = ( I₁+ I₂)?

28.49 -I₂(10.4) = (3.7+ I₂)(-2.5)

Solve above equation.

I₂= 4.78 kg.m^2

Moment of inertia of second B = 4.78 kg m²