Final answer:
The angular momentum of the system comprising two balls connected by a rigid rod can be calculated by finding the center of mass, calculating the moment of inertia for each ball, and then multiplying by the angular velocity, summed for both balls.
Step-by-step explanation:
To calculate the angular momentum of the system, we must first find the center of mass of the system. Since the rod is massless and rigid, the center of mass will be located closer to the heavier ball. After determining the center of mass, we can use it to find the radius of rotation for each ball, which will allow us to calculate the moment of inertia for each ball about the common axis. The angular velocity of 150 rpm must be converted into radians per second (1 rev = 2π rad; 1 min = 60 s).
Once the moments of inertia and angular velocity are known, we can calculate the angular momentum using the formula L = I⋅ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. We add the angular momentum of both balls to obtain the total angular momentum of the system. As the rod is massless, it doesn't contribute to the moment of inertia or angular momentum of the system.