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A ring (2 kg, r = 2 m) rotates in a CW direction with initial angular velocity 10 s-1. A disk (8 kg, r = 2 m) rotates in a CCW direction with initial angular velocity 50 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction. What is the initial angular momentum Li of the ring+disk system? What is the final angular velocity ωf of the ring+disk system?

Respuesta :

Answer:

[tex]L_1 = 720 kg- m^2/s[/tex]

[tex]w = 30 s^{-1}[/tex]

Explanation:

a) Moment of inertia of ring

 [tex]  I_1 = mr^2 = 2\times 2^2 =  8 kg -m^2[/tex]

Moment of inertia of disc

[tex]I_2 = \frac{1}{2} mr^2 = \frac{1}{2} \times 8\times 2^2 =  16 kg - m^2[/tex]

inital angular momentum

[tex]L_1 = I_1w_1 +  I_2 w_2 [/tex]

      [tex]= 8\times (- 10) + 16\times 50[/tex]

[tex]L_1 = 720 kg- m^2/s[/tex]

b) By conservation of angular momentum

720 = (8+16) w

solving for w

[tex]w = 30 s^{-1}[/tex]

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