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A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures below show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar’s angular speed about the axis increase at the fastest rate?.

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onyebuchinnaji

The case where the angular speed of the bar will increase at a fast rate is at smaller radius compared to the initial radius from the center of rotation.

Conservation of angular momentum

The principle of conservation of angular momentum states that the total angular momentum of a closed system is always conserved.

[tex]I_i \omega _i = I_f \omega _f[/tex]

where;

  • Ii is initial moment of inertia of the solid sphere
  • If is the final moment of inertia of the solid sphere
  • ωi is the initial angular speed
  • ωf is the final angular speed

[tex]\omega _f = \frac{I_i \omega _i }{I_f} \\\\\omega_f = \frac{(1/2MR_i^2)\omega _i}{1/2 MR_f^2}\\\\\omega _f = \frac{R_i^2 \omega _i}{R_f^2}[/tex]

where;

  • M is mass of the bar
  • R is radius

The angular speed of the bar depends of the moment of inertia of the bar which in turn depends on axis of rotation.

Thus, the case where the angular speed of the bar will increase at a fast rate is at smaller radius compared to the initial radius from the center of rotation.

Learn more about conservation of angular momentum here: https://brainly.com/question/7538238

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