Please show work. I really need to understand how this works. Thank you in advan
ID: 2240961 • Letter: P
Question
Please show work. I really need to understand how this works. Thank you in advance for all the help.
Two kids are sitting on a merry go round that has a mass of m = 100 kg and a radius of r = 1.8 meters. Abe is sitting at the very edge of the merry go round and, Mary is sitting halfwaty between the edge and the middle of the merry go round. The merry go round completes 1 revolution every 4 seconds.
a. Who has the greater angular velocitry, Abe or Mary? Eplain your choice.
b. What is the angular velocity (ie the angular frequency) of the merry go round?
c. Who has the greater tangential velocity. Abe or Mary? Calculate their Vt values.
d. If Mary has a mass of mM = 52 kg and Abe has a mass of mA = 48 kg, what is the moment of inertia for Mary, Abe, and the merry go round (whaich can be treated as a disk)?
e. Friction eventually brings the merry go round to rest. How many revolutions does the merry go round complete if it takes 15 seconds to stop moving?
Explanation / Answer
a) they will have same angular velocity
b) w = 2 pi/4 = pi/2 = 1.57 rad/s
c) vabe =1.8*1.57=2.83 m/s
vmary = 2.83/2 = 1.41 m/s
so abe has greater
d) I Mary = 52*(0.9)^2=42.12
I abe = 48*1.8^2=155.52
Imerry go round = 0.5*100*1.8^2=162
e) w = w0 + alpha t
alpha = -1.57/15=-0.1047
theta = w0 t + 1/2 alpha t^2 = 1.57*15 -0.5*0.1047*15^2=11.77 rad=1.87 rev