Question

Save Answer < Question 6 of 13 > M Two uniform, solid spheres (one has a mass M and a radius Rand the other has a mass M and a radius Ro = 3R) are connected by a thin, uniform rod of length L = 2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia / about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form. M M R I=

Answer 1

M Ro & 10 L = 2R Ro=3R t 11 ति 12 1 I = 2 3 Moment of inertia of this system is, (moment of inertia of rod about axis AB through center of rod), Is + ( Moment of inertia of Aphere of radius Ro about axis AB), Iz ť (moment of inertia of there of radius R about excis AB), Iz I= I t Iz + 13 5 6 I = - 1 ML? 12 M (22)2 = 12 4 MR² 12 1 MR² 3 = (moment of inertia of sphere about center o t(leoduct of mass of sphere times ittees square of distance between two axes

9 2 -2- в) + И 10 1, - 1, + м(9- (2 ме. м (28) 2 ч [3ej+ ме? 18 ще"+ M2 S І, 2 23 че? п, 11 22 MR- S 12 Б 1 4 Tot M міE 7 MR² 2 че + м Б м(28) - 2-мв'я меъ 2 3 3 5 4 Therefore, 5 moment of inertia , I is ІІ, +, +0, І я че? + 23 мк°+1 чR- 5 MR? 1. 30 мк ме-+ 6 Меъ 3 5 3 6 Та 14 м. 3.