Final answer:
To find the moment of inertia of the system, we calculate the individual moments of inertia for each component and then sum them up.
Step-by-step explanation:
The moment of inertia of a system is the sum of the individual moments of inertia of its components. To calculate the moment of inertia of the system, we need to know the masses and radii of each component. For example, if we have m₁ = 0.05 kg, r₁ = 0.4 m, m₂ = 0.5 kg, and r₂ = 0.01 m, we can calculate the moment of inertia as follows:
- Calculate the moment of inertia for each component using the formula I = m × r². For m₁, I₁ = (0.05 kg) × (0.4 m)² = 0.004 kg·m². For m₂, I₂ = (0.5 kg) × (0.01 m)² = 0.00005 kg·m².
- Calculate the total moment of inertia by summing up the individual moments of inertia. I_total = I₁ + I₂ = 0.004 kg·m² + 0.00005 kg·m² = 0.00405 kg·m².
So, the moment of inertia of the system is 0.00405 kg·m².