Question

Four identical balls, each of mass 4.0 kg, are arranged in the xy plane as shown. if a = 30.0 cm, what is the rotational inertia of this system about the y-axis?

Answer 1

The rotational inertia of the system of four identical balls each with a mass of 4.0 kg and positioned 30.0 cm from the y-axis is 5.76 kg·m² about the y-axis.

Step-by-step explanation:

The question asks for the rotational inertia (moment of inertia) of a system of four identical balls each with a mass of 4.0 kg arranged in the xy-plane about the y-axis. Given that the distance from the y-axis to each ball is a = 30.0 cm, we can calculate the moment of inertia using the formula:

I = ∑ mr²

Since each ball is the same distance from the y-axis and has the same mass, the rotational inertia is:

I = 4(mr²)

I = 4(4.0 kg * (0.30 m)²)

I = 4(4.0 kg * 0.09 m²)

I = 4(0.36 kg·m²)

I = 1.44 kg·m² × 4

I = 5.76 kg·m²

Thus, the rotational inertia of this system about the y-axis is 5.76 kg·m².