Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbour, 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 mo

Question

Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbour, 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 ?

TestHub · Accepted Answer

Central penny: I 0 ​ = 2 1 ​ m r 2 . Each outer penny has its centre 2 r away: I = 2 1 ​ m r 2 + m ( 2 r ) 2 = 2 9 ​ m r 2 . I sys ​ = 2 1 ​ m r 2 + 6 × 2 9 ​ m r 2 = 2 55 ​ m r 2 . With m = 2 kg and r = 1 m, I sys ​ = 55 kg m 2 .

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