Question

LUULULU Problem 8.1a-c Calculate the moment of Inertia of the following Symmetric bodies: a) a cube of side L rotating about one edge b) a sphere of radius L rotating about its center of mass c) a sphere of radius L rotating about a point on its Surface

Answer 1

consider the cube rotating about z-aris. consider a small element of mass dm. Calculate the mass of small element - dm =.8 dady dz write the equation for MOI T= S(x+y)paudę dz. 19 = x ya = {{07 Audy dz + fugir de dy dz] dat X VO IPL LL + L L} = 8B x2 2 m. 22 volume of the cube] } mass (m) = P13 J = m. 222 } V = p t the case

solid sphere Considey a small strip of thickness da calculate the mass of the small strip dm = patada The moment of Inertia of the aglindorio small disc di = [am dI =(2) (f22dx) = pa l de {re P(22_x²) } = 1/2 pm (2²-x²)? da Integrate on both sides I= Į PT -(-x2)%dx raxe 1879 at po (LC) 1 MARS TA point Calculate Is • 2 mL² Ang the Mo I about its surface It mR? » 2 m2 ² + mc?