While at a party, a friend challenges you to a game of sorts, where the challeng

Question

While at a party, a friend challenges you to a game of sorts, where the challenge is to remain sitting throughout. He suggests you hold two 10-kg iron barbells as you sit on a barstool that is free to rotate. Your friend has you extend your arms outward so that the barbells are held away from your body. He then starts the stool rotating. Upon reaching an angular speed of 4.56 rad/s, your friend tells you to pull the barbells back toward your chest. Assuming your body has a rotational inertia of about 8.76 kg · m2 without the barbells and your arms are about 0.72 m long, what is your angular speed after you pull the barbells so they are at the center of your chest?

______ rad/s

Explanation / Answer

Angular momentum = moment of inertia * angular speed

Initial angular momentum = 8.76 kg · m2 * 4.56 rad/s + 10kg*(0.72 m)^2*4.56 rad/s + 10kg*(0.72 m)^2*4.56 rad/s = 87.22

Now, after you pull the barbells so they are at the center of your chest, their moment of inertia becomes 0.

So, Final angular momentum = 8.76 kg · m2 * angular speed + 0

So, Final angular momentum = Initial angular momentum = 87.22

So, 8.76 kg · m2 * angular speed = 87.22

So, your angular speed after you pull the barbells so they are at the center of your chest = 9.957 rad/s

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