The radius of gyration of the leg (tibia) is 8 cm. The mass of the leg segment i

Question

The radius of gyration of the leg (tibia) is 8 cm. The mass of the leg segment is 1.5 kg. What is the moment of inertia about the segment’s center of mass? If the center of mass is 43% of the segment length from the knee, what is the moment of inertia about the knee? While performing the above isometric exercise, the cable snapped and allowed the leg to move, what would be the resulting angular acceleration? After accelerating for 0.5 seconds, what is the angular velocity and angular momentum of the leg?

Explanation / Answer

r = radius of gyration = 8 cm = 0.08 m

m = mass of leg segment = 1.5 kg

Moment of inertia is given as

I = mr2 = 1.5 (0.08)2 = 0.0096 kgm2

Given that :

r = 0.43 L

0.08 = 0.43 L

L = 0.186 m

Moment of inertia about the knee is given as

I = mL2/12 = (1.5) (0.186)2/12

I = 0.004325 kgm2

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