A solid sphere, of mass 1.5 kg and radius 5 cm. is connected to the end of a ver

Question

A solid sphere, of mass 1.5 kg and radius 5 cm. is connected to the end of a vertical rod along a y-axis, of mass 2 kg and length 35 cm. The rod can rotate about z-axis passing through the other end, as show in the figure. The moment of inertia about the center of mass: Irod = ML2/12 and Isphere = (2/5)mR2. What is the moment of inertia of the system (sphere + rod) about z-axis? Starting from rest, the system rotates clockwise around the z-axis from the initial vertical orientation, what is its angular speed when it is inverted?

Explanation / Answer

m=1.5kg M=2kg L=35cm r=5cm I(ball)=(2/3)*m*r^2+m(L+r)^2=2425kgcm^2 I(rod)=(ML^2)/12=204.16kgcm^2 I(total)=2629.16kgcm^2 =0.2629kgm^2 mg(L+r)+(Mg*L/2)=0.5*I(total)*w^2 w=8.42rad/sec

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