Question

3 solid spheres (each with R=1.0m &M=1.0kg) are aligned as shown. An axis of rotation A is exactly in the middle of the spheres and perpendicular to the page. Find the total moment of inertia through the axis A.

29)3 solid spheres (each with R 1.00 m and M 1.00 kg) are aligned as shown. An axis of rotation, A, is exactly in the middle of the 3 spheres and is perpendicular to the page Find the total moment of inertia through the axis A (HINT: finding h might be hard. solve it in terms of h for most of the credit) AV h

Answer 1

SOLUTION

Moment of inertia of solid sphere about its centroid, I_s = (2/5)MR² = (2/5)*1*1² = 0.4 kg-m²

Here, h*cos30^o = R/2

or     h= 0.58 m

Moment of inertia of the assembly, I = 3*( I_s + M*h²)

                                                    = 3*( 0.4 + 1*0.58²)

                                                    = 2.21 kg-m²