A disk with moment of inertia I₁ = 40 kg  m² and angular velocity ₁ = 20 rad/s is dropped on to a stationary second disk along the axis of rotation. The second disk has moment of inertia I₂ = 60 kg  m². What is the angular velocity of the two disks? A) 4 rad/s B) 6 rad/s C) 8 rad/s D) 12 rad/s E) 20 rad/s

Question

Quizplus · Accepted Answer

The total angular momentum of the system must be conserved. Before the collision, the angular momentum of the first disk is given by:
L1 = I1 * ω1 = 40 kg*m²/s * 20 rad/s = 800 kg*m²/s

Since the second disk is stationary, its initial angular momentum is zero.

After the collision, the two disks will rotate together with an angular velocity ωf. The total angular momentum of the system is given by:
Lf = (I1 + I2) * ωf

Using the conservation of angular momentum, we can equate the initial and final angular momenta:
L1 = Lf

Substituting the values gives:
800 kg*m²/s = (40 kg*m² + 60 kg*m²) * ωf
ωf = 800 kg*m²/s / 100 kg*m²
ωf = 8 rad/s

Therefore, the angular velocity of the two disks together is 8 rad/s. The correct choice is C.

A Disk with Moment of Inertia I1 = 40 Kg

A Disk with Moment of Inertia I₁ = 40 Kg