Interestingly, there have been several studies using cadavers to determine the moment of inertia of human body parts by letting them swing as a pendulum about a joint. In one study, the center of gravity of a 5.0 kg lower leg was found to be 18 cm from the knee. When pivoted at the knee and allowed to swing, the oscillation frequency was 1.6 Hz. What was the moment of inertia of the lower leg?

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Question:

Interestingly, there have been several studies using cadavers to determine the moment of inertia of human body parts by letting them swing as a pendulum about a joint. In one study, the center of gravity of a 5.0 kg lower leg was found to be 18 cm from the knee. When pivoted at the knee and allowed to swing, the oscillation frequency was 1.6 Hz. What was the moment of inertia of the lower leg?

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Answer:0.08735 kgm²Explanation:m = Mass of lower leg = 5 kgL = Length of leg = 18 cmg = Acceleration due to gravity = 9.81 m/s²f = Frequency = 1.6 HzI = Moment of inertiaTime period is given by[tex]T=2\pi\sqrt{\dfrac{I}{mgL}}[/tex]Also[tex]T=\dfrac{1}{f}[/tex]So,[tex]I=\dfrac{mgL}{(2\pi f)^2}\\\Rightarrow I=\dfrac{5\times 9.81\times 0.18}{(2\pi 1.6)^2}\\\Rightarrow I=0.08735\ kgm^2[/tex]The moment of inertia of the lower leg is 0.08735 kgm²

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