A reasonable estimate of the moment of inertia of an ice skater spinning with her arms at her sides can be made by modeling most of her body as a uniform cylinder. Suppose the skater has a mass of 64 kg . One eighth of that mass is in her arms, which are 60 cm long and 20 cm from the vertical axis about which she rotates. The rest of her mass is approximately in the form of a 20-cm-radius cylinder.A. Estimate the skater's moment of inertia to two significant figures.B. If she were to hold her arms outward, rather than at her sides, would her moment of inertia increase, decrease, or remain unchanged?

Respuesta :

Answer:

Explanation:

The body can be split into two parts

1 ) cylinder part of mass 7/8 x 64 = 56 kg of radius 20 cm

2 ) In the form of rod attached with cylinder having length 40 cm and mass

of 1/8 x 64 = 8kg

moment of inertia of cylinder

= 1/2 mr²

= .5 x 56 x ( 20 x 10⁻²)²

= 1.12 kg m²

moment of inertia of rods

= 1/3 ml²

= 1/3 x 8 x ( 40 x 10⁻²)²

= .4267 kg m²

Total MI = 1.5467 Kg m²

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