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Crusher8576
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I've been trying this problem for a while now and can't seem to get the given answer. I know I'm probably making an elementary mistake somewhere but I can't find it.
A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis. A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.176 m/s with respect to the track. What is the angular speed of the wheel if its mass is 1.97m and its radius is 0.584 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.) (Answer 0.101 rad/s)
Ok so:
Vt= .176 m/s
mt= M
m2= 1.97M
r= 0.584m
I2=m2r2
Xf= ?
(X is angular velocity, subscript t for train and 2 for wheel)
L=IX=rmv
Li=Lf
Lt+L2=0
So I set it up with the initial equation
Lt = -L2
rmtvt = IX
Then expanded and substituted for corresponding masses
rMv = 1.97Mr2X
M cancels and so does an r, so
vt = 1.97rX
Then substitute the values
.176 = 1.97(.584)(X)
I get a final answer of
X = .153 rad/s
The answer is supposed to be .101 rad/s which I can't seem to get.Also I used X for angular speed instead of omega because the text formatting wasn't working, and about 4 different symbols showed up instead of omega. Not sure why.
Homework Statement
A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis. A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.176 m/s with respect to the track. What is the angular speed of the wheel if its mass is 1.97m and its radius is 0.584 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.) (Answer 0.101 rad/s)
Ok so:
Vt= .176 m/s
mt= M
m2= 1.97M
r= 0.584m
I2=m2r2
Xf= ?
(X is angular velocity, subscript t for train and 2 for wheel)
Homework Equations
L=IX=rmv
Li=Lf
Lt+L2=0
The Attempt at a Solution
So I set it up with the initial equation
Lt = -L2
rmtvt = IX
Then expanded and substituted for corresponding masses
rMv = 1.97Mr2X
M cancels and so does an r, so
vt = 1.97rX
Then substitute the values
.176 = 1.97(.584)(X)
I get a final answer of
X = .153 rad/s
The answer is supposed to be .101 rad/s which I can't seem to get.Also I used X for angular speed instead of omega because the text formatting wasn't working, and about 4 different symbols showed up instead of omega. Not sure why.
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