Find-moment-of-inertia-of-the-area-bounded-by-the-curve-r-2-a-2-cos2-about-its-axis-

Question Number 44526 by arnabmaiti550@gmail.com last updated on 30/Sep/18

Find moment of inertia of the area bounded

by the curve r^{2} = a^{2} \cos 2 θ

about its axis

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Oct/18

Answered by ajfour last updated on 30/Sep/18

I = \int_{0}^{2 π} [\int_{0}^{r} ρ r^{2} (r d r)] d θ

= \frac{ρ}{4} \int_{0}^{2 π} a^{4} \cos^{2} 2 θ d θ

= \frac{ρ a^{4}}{8} \int_{0}^{2 π} (1 + \cos 4 θ) d θ

= \frac{ρ a^{4} π}{4} .

Commented by arnabmaiti550@gmail.com last updated on 01/Oct/18

please explain the first line

Commented by ajfour last updated on 01/Oct/18

I = \int r^{2} d m = \int r^{2} ρ (d A)

A i s a r e a, ρ i s m a s s p e r u n i t a r e a .

I = \int_{0}^{2 π} ρ r^{2} (r d r) d θ .

Commented by arnabmaiti550@gmail.com last updated on 01/Oct/18

Thank u sir . Now I can understand