Exercise
https://texercises.com/exercise/change-of-angular-velocity/
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The following quantities appear in the problem: Masse \(m\) / Kraft \(F\) / Radius \(r\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) /
The following formulas must be used to solve the exercise: \(F = mr\omega^2 \quad \)
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Exercise:
A body revolves on a path. Then its mass is doubled the radius of the circular path is halved and three times as much force is now required to keep it on the path as in the first case. By what factor did the angular velocity change?

Solution:
omega_ sqrtfracF_m_r_ omega_ sqrtfracF_m_r_ sqrtfracF_m_ frac r_ SolQtyfsqrt N fracomega_omega_ frac sqrt fracF_m_ frac r_ sqrt fracF_m_r_ sqrtfracfracF_m_r_fracF_m_r_ sqrt fracF_m_r_ fracm_r_F_ sqrt approx f
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Exercise:
A body revolves on a path. Then its mass is doubled the radius of the circular path is halved and three times as much force is now required to keep it on the path as in the first case. By what factor did the angular velocity change?

Solution:
omega_ sqrtfracF_m_r_ omega_ sqrtfracF_m_r_ sqrtfracF_m_ frac r_ SolQtyfsqrt N fracomega_omega_ frac sqrt fracF_m_ frac r_ sqrt fracF_m_r_ sqrtfracfracF_m_r_fracF_m_r_ sqrt fracF_m_r_ fracm_r_F_ sqrt approx f
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Tags
kinematik, kreisbewegung, mechanik, physik, winkelgeschwindigkeit
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Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Algebraic
Creator uz
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File
Link