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Jessica stretches her arms out 0.8 m from the center of her body while holding a 2.0 kg mass in each hand. She then spins around on an ice rink at 1.2 m/s.
a. What is the combined angular momentum of the masses?
b. If she pulls her arms in to 0.12 m, what is her new linear speed?

Respuesta :

Answer:

a) L = 3.84 kg m² / s, b)   v = 0.96 m / s

Explanation:

a) the angular momentum is

    L = I w

Linear and angular magnitudes are related

     v = w r

     w = v / r

The moment of inertia of a point mass is

      I = m r²

We replace

     L = 2 m r² v / r

The two is because they are two masses

     L = 2 m r v

     L = 2 2.0 0.8 1.2

     L = 3.84 kg m² / s

b) The girl reduces the distance to 0.12 m

In this case the system is isolated, so the angular momentum is preserved

Initial moment,

       L₀ = 3.84 kg m² / s

Final after shrugging arms

       [tex]L_{f}[/tex] = I  [tex]w_{f}[/tex]

       L₀ =  [tex]L_{f}[/tex]

      3.84 = 2 2.0 0.12 wf

       [tex]w_{f}[/tex]  = 3.84 / 0.48

       [tex]w_{f}[/tex]  = 8 rad / s

Linear velocity is

       v = w r

      v = 8 0.12

      v = 0.96 m / s

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