CLASSICAL MECHANICS PHYS 105B
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This 1 page Class Notes was uploaded by Hailey Halvorson on Thursday October 22, 2015. The Class Notes belongs to PHYS 105B at University of California Santa Barbara taught by J. Martinis in Fall. Since its upload, it has received 12 views. For similar materials see /class/227125/phys-105b-university-of-california-santa-barbara in Physics 2 at University of California Santa Barbara.
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Date Created: 10/22/15
01 92 A wheel rolling at speed 1 will have angular velocity 0 vT If we consider this problem by using the CoM the KB is the sum of the COM translational motion plus the rotation around the COM So 7 2 l 2 2 2 27 2 KEing 2140 72Mv 22MR vT 74Mv Now we can also consider the point of the wheel touching the ground The special feature of this point is that it is momentarily at rest Therefore all the kinetic energy is due to the rotational motion around that point If we remember the parallel axis theorem 1 10M Mh2 where h is the distance from the CoM to the translated axis we get that 1 around this point is 32MR2 So 7127 2 KEiglw 74Mv This is identical to what we found above 02 99 Well do this integral in cylindrical coordinates in which the volume element is dV pdp d9 d2 So L 27r R I d2 d9 dpp p2 0 0 0 R M 27f L d 3 7 M lt m 1 7MP 2 The products of inertia are zero due to the re ective symmetry of a cylinder across the z 7 2 and y 7 2 planes When we integrate over a mass distribution that is even in z and y multiplied by a single factor of z or y which will be odd we get an integral over an odd function which is necessarily zero 03 910 031 a L M271 2 Adzfz igML
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