While at a party, a friend challenges you to a game of sorts, where the challeng
ID: 1437229 • Letter: W
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-kgiron 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 4.98 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 0.88 m long, what is your angular speed after you pull the barbells so they are at the center of your chest?
Explanation / Answer
Angular momentum,
L = I …………..equation 1
Where,
L is the angular momentum,
I is moment of inertia of the rotating body about axis of rotation,
is the angular velocity.
Given values :
I = 8.76 kg · m2
=4.98 rad/s
Therefore,
Angular momentum is,
L = 8.76 * 4.98
= 43.62 kg. m2/s
Now, along with 10 kg iron bar and arm distance 0.88 m long, we can calculate the moment of inertia for this situation.
Therefore,
I = m*r2 = 10 * (0.88)2
= 7.744 kg. m2
From equation 1,
L = I , therefore,
= L / I
= 43.62 / 7.744
= 5.63 rad/s
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