Stan.\'s leg and foot together have a mass of 10.5 kg. The leg and foot together

Question

Stan.'s leg and foot together have a mass of 10.5 kg. The leg and foot together are 90 cm long. The muscle is attached 1/9 of the way along the leg (10 cm from the hip joint). At the moment shown (60 degrees from the vertical), Stan.'s leg is swinging forwards with a clockwise angular acceleration of 0.2 rad/s2.

1) We assume that the psoas major muscle is the only muscle responsible for lifting the leg. 2) We assume that the leg plus foot can be modeled as a thin, uniform rod, rotating about one end (at the hip joint). A uniform rod has its centre of mass at the middle. That is where the gravitational force will act on the leg.The rotational analog of Newton's second law determines the rotational motion of the leg. Write the law into your logbook too. As you can see, we will need to know the rotational inertia of the (leg+foot). Calculate the rotational inertia first. Use three significant figures so we can round to two later with confidence

Explanation / Answer

Rotational inertia of rod about the center of mass=1/12 mL2

using parallel axis theorem, rotational inertia about the end of rod= 1/12mL2+ m (L/2)2= 1/3 mL2

so moment of inertia of Leg about the Hip joint=1/3 (10.5)(0.9)2

moment of inertia of Leg about the Hip joint=2.84 kgm2

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