Question

3. In the following figure, a circular disk with a hole that's eccentrically placed is shown. The disk had an areal density p (mass per unit area) and rı = Express the mass moment of inertia (in-plane rotation), about O, in terms of p and r2.

Answer 1

Golnion XL- D far x unit per area of Original disc = .. mass of orginal = 4 aisc M=822² Radius of Smaller disc = 8 Giren 8, = 82/4 Mass 7 smallen disc = on 8,2 = y 24744)? a M/ So, a masses are M / concentrated at o Concentrated o? mans is - ve as it is removed pom the disc 46 ML CS Scanned with -Care Seamer

mass moment of inesten of bigge disc about és ponies of rotation is given by (Tel) biny Moz? Mass moment of inertia y Smaller wise about the aris of sotahon ato can be found sy parallel axis theorem . Ed Small (10) + m (&?;) (Tolsmaller z moi + m (27.2 2 EMO 16 M 2 + M x 48,2 IC min mygo 16' 2 = 9 M2,2 32 Mass moment of inertia of given ting in plane of rotation about o. = (10) bigget to) smaller 2 9 Mr, 2 32 Les camscanner Scanned with Camscanner

2 Merz 9 Miro 32 hos) = M822 - 9 32X16 Mr2 256 M22²-9992² 512 = 347 M22² 512 =947 yaray 512 MOT =1.1part CS Scanned with