The figure shows a hollow cylindrical tube that has a mass M, a length L, and a

Question

The figure shows a hollow cylindrical tube that has a mass M, a length L, and a moment of inertia ML2/10. Inside the cylinder are two disks, each of mass m, separated a distance , and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. You are designing this cylinder-disk apparatus to shut down the rotations by triggering an electronic "shutoff" signal (sent to the rotating motor) when the strings break and the disks hit the ends of the cylinder. During development, you notice that with the system rotating at some critical angular speed ?, the string suddenly breaks. When the disks reach the ends of the cylinder, they stick. Obtain expressions for the final angular speed and the initial and final kinetic energies of the system. Assume that the inside walls of the cylinder are frictionless. (Use any variable or symbol stated above as necessary.)

Final angular speed
Final kinetic energy

Initial kinetic energy

Explanation / Answer

moment of inertia of the two disks is mr^2. (2*mr^2/2). so that conservation of angular momentum. ML^2*w0/10=(ML^2/10+mr^2)*w where w0 be initial angular velocity and w be final velocity kinetic energy. K=I*w^2/2=(ML^2/10+mr^2)*(ML^2*w0/10(ML^2/10+mr^2))^2/2 K_final=(ML^2*w0/10)^2/(2*(ML^2/10+mr^2)) -------------- K_initial=ML^2*w0^2/20

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