Can you please help with either of these? I know the answers, but want to unders
ID: 1782351 • Letter: C
Question
Can you please help with either of these? I know the answers, but want to understand the process. Thanks!
115. •Medical. together accoun head is 7.0% an We can model a Medical, Sports On average both arms and hands account for 13% of a person's mass, while the 70% and the trunk and legs account for 80%. model a spinning skater with his arms out- hed as a vertical cylinder (head + trunk + legs) Two solid uniform rods (arms + hands) extended Montally. Suppose a 62-kg skater is 1,8 m tall, has ms that are each 65 cm long (including the hands), and arrunk that can be modeled as being 35 cm in diameter. Tf the skater is initially spinning at 70 rpm with his arms Outstretched, what will his angular velocity be (in rpm) when he pulls in his arms until they are at his sides paral- lel to his trunk?Explanation / Answer
115.
Mass of torso = mass of head + mass of trunk + mass of legs
Mtorso = 0.8m + 0.07m = 0.87*m
Mtorso = 53.94 kg
Marms = 0.065*62 = 4.03kg
r = 0.35 / 2 = 0.175 m
L = 0.65 m
lnitial moment of inertia,
l = (1/2)*Mtorso*r^2 + 2*[(1/2)*Marms*L^2 + Marms*(r + L/2)^2]
l = (1/2)* 53.94*(0.175)^2 + 2*[(1/2)*4.03*0.65^2 + 4.03(0.175 + 0.325)^2
l = 4.54 kg.m^2
llnitial abgular momentum,
Li = l*w = 4.54*70
Li = 318.05
Final moment of inertia,
lf = (1/2)*Mtorso*r^2 + 2* 2*Marms*r^2
lf = (1/2)*53.94*(0.175)^2 + 2*4.03*0.15^2
lf = 0.788 kg.m^2
Final angular momentum,
Lf = lf * w
Lf = 0.788 * w
From law of momentum conservation,
Li = Lf
318.05 = 0.788*w
w = 403.61 rad/s