Dr Bubar has advanced to the American Ninja Warrior semifinals! During this phas
ID: 1417819 • Letter: D
Question
Dr Bubar has advanced to the American Ninja Warrior semifinals! During this phase, there is an obstacle that spins him rapidly on a turntable. He starts out spinning with his arms tucked in, at an angular velocity of 10.0 radians per second. When he throws his arms out, what happens to his angular velocity (Choose 1, 2 or 3)? He speeds up He slows down Angular momentum is conserved so he goes the same angular velocity. Now lets play with some numbers. Imagine each of his arms is a thin, uniform rod of length 0.80 m and mass 4.0 kg hinged at his shoulders, which are 0.20 meters from the center of his body. Perform the following calculations. What is the moment of inertia of the Dr Bubar with his arms out? What is the angular momentum of the Dr Bubar with his arms out? What is the moment of inertia of Dr Bubar with his arms in? What is the angular velocity of Dr Bubar with his arms in? What is the angular momentum of Dr Bubar with his arms in?Explanation / Answer
(a) When he throws his arms out the moment of inertia will increase therefore the angular velocity will decrease.
hence he slows down.
(b) Moment of inertia of the arms about shoulder = ML2/12 = 0.213kg-m2
Now both arm will have = 2*0.853 = 0.4267 kg-m2
Moment of Inertia of the body = 2ML2/12 + 2(Mr2) where r is the distance of the centre of body and arm.
Moment of Inertia of body = 0.4267 + 2(4*0.62) = 3.3067 kg-m2
(c) Angular momentum = IW = 3.3067*W= 3.3067 W
where W is angular velocity which we can calcualte by the conservation of angular momentum
3.3067W = 3.2 (for this check last step)
W = 0.967 rad/s
(d) Moment of inertia = 2Mr2 where r = 0.2
= 2*4*0.22 = 0.32 kg-m2
(e) Angular velocity is given as 10 rad/s when arms are in
(f) Angular momentum = IW where W is angular velocity
= 0.32*10 = 3.2
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