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 0, in terms of p and r2. tot

Answer 1

the answer to this question is

$\frac{251\rho \pi r_{2}^{4}}{256}$

SHEET NO 5 IS GIVEN for REFRENCE ONLY.
Saulation 3 Sheet 0 This is on compound abject. It moment Canbe calculated monsent of second dink from Ist. by subtracting M2 2 120 Iz to to r & 3 Dr 4 = 2 2 2 28 = 5 2 0 f to Y. Is I 30 - Izo Ile Iis Moment with resput to 'o'

Shut - Inquestion given M2 mi areal density = f = TR 8 = 2 4 we know that mass moment dink about its centraid is given by 3 yum by of I= m R² If mass durity is given than m = SA A=tr ( for dire) m = Saga Now mass manent Aneshia became مج I= (878) (8) I Sa84 And we know the panelles en theoreme Io = I g + ma² m = tatal mass a = 1 distance betuisen point and Centroid, Io = Mass moment anestia about the Centroid and 1

Sheet Now from dixe 1 Ile= IT8,4 Io = Iest maz here M = STRE a=28 (from final and Io = strt + 1878, 2) (28) Iso = strta Ugart I, = 5gart for dine ② I 2o = I2G= sar4 I=8T84

Sheet NowNe have Iz = I₂ I, = ST - 58504 (r = 0 8 / C given) Sart -53T 4 Sart - 5 8787 256 Iz 251 Sara 256
SSHEET NO 5