To solve the problem, conservation of angular momentum is applied. The initial angular momentum of the first disk is calculated, and after adding the second disk, the new combined moment of inertia is determined. The final angular speed is found by equating the system's initial and final angular momentum.
The student asks about the final angular speed of a composite system of two disks that are combined together after one, initially non-rotating, is dropped onto a spinning disk. To find the final angular speed, we apply the conservation of angular momentum, which states that if no external torques act on a system, the total angular momentum of the system remains constant.
First, we calculate the initial angular momentum of the rotating disk, using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. We convert the given angular speed from revolutions per second (rev/s) to radians per second (rad/s) by multiplying by 2π since there are 2π radians in one revolution. Then, we compute the combined moment of inertia of both disks combined. Using the conservation of angular momentum, we can solve for the final common angular speed of the system.
So, by setting the initial angular momentum equal to the final angular momentum of the composite system and solving for the final angular speed, we can find the final answer in 2 lines.