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Asked Nov 17, 2019
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Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R=2.68 m. Disk 1 has a moment of inertia I_1=11.1 kg⋅m2. Disk 2 has a moment of inertia I_2=16.6 kg⋅m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω_1,z=10.3 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω_2,z=−15.5 rad/s.

*Common angular velocity: ω_common,z = -5.161 rad/s

  • How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small.
Disk 1
Disk 2
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Disk 1 Disk 2

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Step 1

Apply conservation of angular momentum for the discs, and solve for the common final angular ve...

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1,1,0 ,) C,Z (11.1 kg m2 (10.3 rad/s)+(16.6 kg -m2)(-15.5 rad/s) (11.1 kg m2(16.6 kg m2) =-5.161 rad/s

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