The picture above shows a rotating disk of mass M and radius R. The timer is use

Question

The picture above shows a rotating disk of mass M and radius R. The timer is used to determine the time for one rotation, T, used to get the angular velocity omega. The initial angular momentum of the system, L_i, is the product of the moment of inertia, I_i and initial angular velocity, omega_i, of the rotating disk. Then a new, non-rotating ring of mass m and radius r is carefully dropped onto the rotating disk. The whole system now rotates with a slower final angular velocity because of the new total moment of inertia, I_f, is now the sum of the moments of inertia of the disk and ring. Fill in the blanks with the appropriate expressions using the elements mentioned above. Show your work. Conservation of angular momentum requires L_i = L_f or equivalents I_f, omega_i = I_f omega_f Initially we only have the disk rotating, with I_i = I disk =, where omega_i = then we have the disk and the ring with I_f = I_disk + I_ring =__and omega_f =__ In this week's workshop, you will Find the moments of inertia and the angular velocities, and check that angular momentum has been conserved, i.e. I+f omega_f = I_f omega_f

Explanation / Answer

1) Ii= Idisk= 0.5*M*R2

2) wi= 2*pi/T

3) If= Idisk+ Ir= 0.5*M*R2+ 0.5* m*r2

4) wf= 2*pi/ T"

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