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Two solid disks are rotating without friction around a vertical axis. Disk 1, mass m1, radius r1, rotates at an angular speed ω1 (counter clockwise is positive). Disk 2, mass m2, radius r2, rotates at an angular speed ω2. Disk 1 slides down the axis, and lands onto disk 2, after which they rotate together. a)  Determine their common angular speed, ω, after the collision. b)  Give the value of ω1 in terms of ω2 and other variables, such that there is no rotation at the end. c)  Express the difference between the total rotational kinetic energy before and after in terms of (ω1-ω2)2 in a concise form and show that it is ≤ 0.

Two solid disks are rotating without friction around a vertical axis. Disk 1, mass m1, radius r1, rotates at an angular speed ω1 (counter clockwise is positive). Disk 2, mass m2, radius r2, rotates at an angular speed ω2. Disk 1 slides down the axis, and lands onto disk 2, after which they rotate together. a)  Determine their common angular speed, ω, after the collision. b)  Give the value of ω1 in terms of ω2 and other variables, such that there is no rotation at the end. c)  Express the difference between the total rotational kinetic energy before and after in terms of (ω1-ω2)2 in a concise form and show that it is ≤ 0.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Two solid disks are rotating without friction around a vertical axis. Disk 1, mass m1, radius r1, rotates at an angular speed ω1 (counter clockwise is positive). Disk 2, mass m2, radius r2, rotates at an angular speed ω2. Disk 1 slides down the axis, and lands onto disk 2, after which they rotate together.

  1. a)  Determine their common angular speed, ω, after the collision.

  2. b)  Give the value of ω1 in terms of ω2 and other variables, such that there is no rotation at the

    end.

  3. c)  Express the difference between the total rotational kinetic energy before and after in terms

    of (ω1-ω2)2 in a concise form and show that it is ≤ 0. 

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Transcribed Image Text:100 ول)
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