Question

g Three unequal point masses are attached to a vertical shaft with light rods. Two masses, m and 3m, are at a distance a from the shaft. The third mass, 2m, is at a distance 2a from the shaft. The three masses and the shaft rotate as a single unit about the vertical axis through the shaft. What is the moment of inertia of this system about the vertical axis

Answer 1

12ma²

Step-by-step explanation:

The moment of inertia I = ∑mr² where m = mass and r = distance from shaft

Since we have three masses,

So, I = m₁r₁² + m₂r₂² + m₃r₃² where m₁ = first mass = m, m₂ = second mass = 3m and m₃ = third mass = 2m. Also, r₁ = distance of first mass from shaft = a, r₂ = distance of second mass from shaft = a and r₃ = distance of third mass from shaft = 2a.

I = m₁r₁² + m₂r₂² + m₃r₃²

I = ma² + 3ma² + 2m(2a)²

I = ma² + 3ma² + 2m(4a²)

I = ma² + 3ma² + 8ma²

I = 12ma²