Consider a person who is sitting on a frictionless rotating stool as in the figu

Question

Consider a person who is sitting on a frictionless rotating stool as in the figure below. The person initially has his arms outstretched and is rotating with an angular speed of 5.2 rad/s. He then pulls his arms close to his body. (For simplicity, model the person as two separate parts: The sitting legs, head, and torso have a fixed mass and radius and can be modeled as a cylinder, and both arms can be modeled as a single bar of changeable length but constant mass spinning around its center) Initial position Final position (a) Estimate the person's arm span when his arms are outstretched. Estimate the person's arm span when his arms are tucked in. Estimate the radius of the person's torso Estimate the mass of the person's torso. kg Estimate the mass of the person's arms. kg Calculate his final angular speed. (Use your estimates.) rad/s (b) Calculate the kinetic energy before and after the person pulls his arms into his body. (Use your estimates.) KEbefore KE after =

Explanation / Answer

a)1.8 metres - Stretched Arm Span (L)

0.4 metres - Arms tucked in (L1)

0.3 metres - Radius of torso (R)

70 Kgs - Mass of torso (M)

8 Kgs - Mass of Arms (m)

Conservation of Angular momentum will be used.

I1w1 = I2w2

I1 is Moment of Inertia when arms are outstretched. = MR^2/2 + mL^2/12

I1 = 5.31 Kg m^2

I2 is Moment of Inertia after his arms are tucked in = MR^2/2 + mL1^2/12

I2 = 3.26 Kg m^2

w1 and w2 are initial and final angular velocities.

w2 = 8.47 rad/s

b) KE1 = (1/2)I1w1^2 = 71.79 J (Before)

KE2 = (1/2)I2w2^2 = 116.94 J (After)

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