center of mass with two points

Question

If m₁ = 5.00 kg is located at x₁ = -9.70 m and m₂ = 12.0 kg is located at x₂ = 10.9 m, then

B. How far is each mass from the center of mass?

r₁ =  m

r₂ =  m

C. What is the system's moment of inertia about an axis through the center of mass and perpendicular to the x-axis?

I =  kg m²

Answer 1

A. x_C = (m₁x₁ + m₂x₂)/(m₁ + m₂) = (5·(-9.7) + 12·10.9)/(5 + 12) = 3.56m

B. r₁ = 3.56 - (- 9.70) = 13.26m; r₂ = 10.9 - 3.56 = 7.34 m

C> I = m₁r₁² + m₂r₂² = 5·13.26² + 12·7.34² = 1525.65 kgm².