A solid disk of mass m 1 = 9 kg and radius R = 0.24 m is rotating with a constan
ID: 1448585 • Letter: A
Question
A solid disk of mass m1 = 9 kg and radius R = 0.24 m is rotating with a constant angular velocity of = 31 rad/s. A thin rectangular rod with mass m2 = 3.4 kg and length L = 2R = 0.48 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?
2.
What is the initial rotational energy of the rod and disk system?
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 = 5.8 s to accelerate to its final angular speed with the disk. What average torque was exerted on the rod by the disk?
Explanation / Answer
given data:
disk mass m1 = 9 kg and radius R = 0.24 m, ? = 31 rad/s.
rod mass m2 = 3.4 kg and, length L = 2R = 0.48 m
1.
What is the initial angular momentum of the rod and disk system?
I_disk = ½*m1*R² = ½ * 9kg * (0.24m)² = 0.2592 kg·m²
I_rod = m2*L²/12 = 3.4kg * (0.48m)² / 12 = 0.0653 kg·m²
2.
What is the initial rotational energy of the rod and disk system?
KE =½ * I_disk * ?2= ½ * 0.2592kg·m² * (31rad/s)² = 124.54 J
3.
What is the final angular velocity of the disk?
angular momentum is,
L = I_disk * ? = 0.2592kg·m² * 31rad/s = 8.0352 kg·m²/s
8.0352 kg·m²/s = (0.2592 + 0.0653)kg·m² * ?'
?' = 24.76 rad/s
4.
What is the final angular momentum of the rod and disk system?
L = I_disk * ? = 0.2592kg·m² * 31rad/s = 8.0352 kg·m²/s
5.
What is the final rotational energy of the rod and disk system?
KE' = ½ * (0.2592 + 0.0653)kg·m² * (24.76rad/s)² = 99.46 J
6.
The rod took t = 5.8 s to accelerate to its final angular speed with the disk. What average torque was exerted on the rod by the disk?
? = (?' - ?o) / t = (24.76 - 0)rad/s / 5.8s = 4.268 rad/s²
? = I? = 0.0653kg·m² * 4.268rad/s² = 0.2787 N·m
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