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A professor sits on a rotating stool that is spinning at 10.010.0 rpm while she holds a heavy weight in each of her hands. Her outstretched hands are 0.7050.705 m from the axis of rotation, which passes through her head into the center of the stool. When she symmetrically pulls the weights in closer to her body, her angular speed increases to 28.528.5 rpm. Neglecting the mass of the professor, how far are the weights from the rotational axis after she pulls her arms in?

Respuesta :

opudodennis

Answer:

0.4176 m

Explanation:

L: angular momentum

Just as [tex]p= mv[/tex], [tex]L = I\omega[/tex], I = sum of [tex]mr^{2}[/tex]

[tex]L_o=2mr_o^{2}\omega_o[/tex]

[tex]Lf = 2mrf^{2}\omega_f[/tex]

we know [tex]r_o = 0.705 m[/tex]

[tex]\omega_o = 10 * 2\pi[/tex] rad per minute, and [tex]\omega_f = 28.5 * 2\pi[/tex] rad per minute

[tex]rf = r_o\sqrt{\frac {\omega_o}{\omega_f}} = 0.705 * \frac {10.0}{ 28.5}[/tex]

rf = 0.4176 m

johanrusli

The weights are as far as 0.418 m from the rotational axis after she pulls her arms in

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Further explanation

Let's recall Angular Momentum formula as follows:

[tex]\boxed {L = I \omega}[/tex]

where:

L = angular momentum ( kg.m²/s )

I = moment of inertia ( kg.m² )

ω = angular frequency ( rad/s )

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Given:

initial angular frequency = ω₁ = 10.0 rpm

initial radius of rotation = R₁ = 0.705 m

final angular frequency = ω₂ = 28.5 rpm

Asked:

final radius of rotation = R₂ = ?

Solution:

We will use Conservation of Angular Momentum to solve this problem:

[tex]L_1 = L_2[/tex]

[tex]I_1 \omega_1 = I_2 \omega_2[/tex]

[tex](2m (R_1)^2) \omega_1 = (2m (R_2)^2) \omega_2[/tex]

[tex](R_1)^2 \omega_1 = (R_2)^2 \omega_2[/tex]

[tex](0.705)^2 \times 10.0 = (R_2)^2 \times 28.5[/tex]

[tex]R_2 = \sqrt{ \frac{10.0}{28.5} \times (0.705)^2 }[/tex]

[tex]R_2 \approx 0.418 \texttt{ m}[/tex]

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Conclusion:

The weights are as far as 0.418 m from the rotational axis after she pulls her arms in

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Learn more

  • Impacts of Gravity : https://brainly.com/question/5330244
  • Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
  • The Acceleration Due To Gravity : https://brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics

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