In a popular demonstration, a person sits on a rotation stoll ( like the one we

Question

In a popular demonstration, a person sits on a rotation stoll ( like the one we have used in class) holding a 2 kg mass in each hand. initially, the stool is rotating slowly and the person's arms are outstrechted, as shown in the picture below at left. the person then pulls in their arms to bring the weights close to the center of their body, as show below at right.

a) when the person pulls in their arms does their angular speed increase, decrease, or remain constant? explain why this happens.

B) Make a numerical estimate for the moment of inertia of the stool, clearly explaining your reasoning and assumptions. ( the stool will be out at the front of the classroom; you may walk up to examine it at any point)

In a homework problem, we estimated that the moment of inertia of a person wth outstretched arms was about 2.5 kgm^2. Suppose that in the initial situation ( in the picture on the left), the stool takes about 4 second to make one revolution.

3, In a popular demonstration, a person sits on a rotating stool (nike the ame we bave used in class) bolding a 2-kg mass in each hand. Initially, the stool is rotating slowly and the person's arms are outstretched, shown in the picture below at left, The person then pulls in their arms to bring the weights clase to the center of their body, as shown below at right. (a) 6 points) When the person pulls in their arms, does their abgular speed increase, decreose, or remain constant? Explain why tbls happens. (b) (6 points) Make a numerical estimate for the moment of inertia of the stool, clearly explaining your reasoning and assumptions. (The stool will be out at tbe front of the classroom you may walk up to examine it at any point In a homework problem, we estimated that the moment of inertia of a person with outstretched arms was about 2.5 kg m2. Suppose that in the initial situation (in the picture on the left), the stool takes about 4 seconds to make one revolution. (c) 8 points) Use the given information, along with your result from part (b), to estimate the angular speed of the stool after the person pulls in their arms. As always, show your work and explain your reasoning and assumptions. Page 5 of 8

Explanation / Answer

3

a)

as the person pull in the arms, the moment of inertia of the system decreases. as we know that the angular momentum is constant and is given as

L = I w

so as the moment of inertia "I" decreases , the value of "w" increases so as to keep the angular momentum "L" constant.

hence the angular speed increases.

b)

I = moment of inertia of person

I' = moment of inertia of each mass in each hand

w= initial angular speed

w' = final angular speed

using conservation of angular momentum

(I + 2 I') w = I w'

w' = (I + 2 I') w / I

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