Angular momentum urgent help

Question

a solid disk of mass m1 = 8.5 kg and radius R = 28 cm is rotating with a constant angular velocity of ω = 28 rad/sec. A thin rectangular rod with mass m2 = 3.5 kg and length L = 56 cm begins at rest above the disk and is dropped on the disk where it skids and eventually spins with the disk.

1- Circle the correct answer:

In this interaction, angular momentum is ( conserved / not conserved ) and rotational kinetic energy is ( conserved / not conserved ).

2- What is the initial angular momentum of the rod and disk system?

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

4- The rod took t = 5.2 s to accelerate to its final angular speed with the disk. What average torque was applied to the rod by the disk?

Answer 1

1- Circle the correct answer:

In this interaction, angular momentum is (conserved / not conserved) and rotational kinetic energy is (conserved / not conserved). Rotational kinetic energy is not conserved, as the mass and its distribution of rotation object is changed.

 As for angular momentum, it is conserved, as there is no additional external torque.

2- What is the initial angular momentum of the rod and disk system? If initially the rod is at rest, then L_system= L_disk=I_disk ω₁=(1/2)m₁R² =(8.5*0.28²*28)/2=9.33 kgm²/s

3- What is the final angular velocity of the disk? I_diskω₁= (I_disk +I _rod)ω₂=[(1/2)m₁R² +(1/3)m₂L²]ω_2; now, calculate ω₂=

4- The rod took t = 5.2 s to accelerate to its final angular speed with the disk. What average torque was applied to the rod by the disk? τ=αI_disk+rod, α=∆ω/∆t =(ω₂-ω₁)/(5.2 s) now, calculate τ=