Answer to Question #195323 in Physics for mazzu

Question

Consider point objects each with mass 1.0 kg positioned at the corners of

an equilateral triangle with side 1.0 m.

1.) What is the total moment of inertia

of the point objects about an axis perpendicular to the triangle and passing

through the center?

2.) Use parallel-axis theorem to calculate the total amount of intertia about an axis perpendicular to the triangle and passing through one of the corners.

Answer 1

$x\cdot\cos30°=1/2=0.5\to x=0.5/\cos30°=0.577\ (m)$

1) $I_0=3\cdot mx^2=3\cdot1\cdot0.577^2=1\ (kg\cdot m^2)$

2) $I=I_0+mx^2=1+3\cdot0.577^2=2\ (kg\cdot m^2)$