Question

A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is rotating with a constant angular velocity of ω = 31 rad/s. A thin rectangular rod with mass m2 = 3.9 kg and length L = 2R = 0.44 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk.
1) What is the initial angular momentum of the rod and disk system?
6.97 kg-m2/s
2) What is the initial rotational energy of the rod and disk system?
108.14 J

3) What is the final angular velocity of the disk?

4) What is the final angular momentum of the rod and disk system?

5) What is the final rotational energy of the rod and disk system?

6) The rod took t = 6.5 s to accelerate to its final angular speed with the disk. What average torque was exerted on the rod by the disk?

Answer 1

We are given with
m1 = 9.3 kg
R = 0.22 m
ω = 31 rad/s
m2 = 3.9 kg
L = 2R = 0.44 m

The angular momentum is determined using the formula
L  = I w
where I is the moment of inertia

For a solid disk
I = (1/4) MR^2
For a rectangular rod
I = (1/12) ML^2

The rotational energy has the formula
E = (1/2) I w^2

Substitute the given values for getting the answers