Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure below. Each penny is a uniform disk of mass m=2 kg and radius r =1 m. What is the moment of inertia of the system (in kg - m 2 ) of seven pennies about an axis that passes through the center of the central penny and is normal to the plane of the pennies?

Question

Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure below. Each penny is a uniform disk of mass m=2 kg and radius r =1 m. What is the moment of inertia of the system (in kg - m 2 ) of seven pennies about an axis that passes through the center of the central penny and is normal to the plane of the pennies? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

I text sys =( mr 2/2)+[( mr 2/2)+ m (2 r )2] × 6 =(55/2) mr 2=55

I sys​=2mr2​+[2mr2​+m(2r)2]×6 =255​mr2=55

$I_{sys} = \frac{m r ^{2}}{2} + [\frac{m r ^{2}}{2} + m (2 r)^{2}] \times 6$
$= \frac{55}{2} m r^{2} = 55$