- #1
BBA Biochemistry
Homework Statement
A horizontal plywood disk with mass 6.90 kg and diameter 1.14 m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.04 m to the disk. A 1.40 −kg , battery-driven model train rests on the tracks. To demonstrate conservation of angular momentum, you switch on the train's engine. The train moves counterclockwise, soon attaining a constant speed of 0.790 m/s relative to the tracks. What is the magnitude and direction of the angular velocity?
Homework Equations
L=rp
L=Iω
v=ωr
The Attempt at a Solution
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As the problem states, this is definitely a conservation of angular momentum problem. The train is a particle with angular momentum, so it's angular momentum is given by L=rp.
Lt=rtps=Lt=rtmsvt
Since the train is part of the system, when it gained this angular momentum, to disk must have also gained an equal amount of angular momentum in the opposite direction.
Ld=Idωd=0.5mdrd2ωd
Ld+Lt=0
Setting them equal to each other gets:
rtmtvt=0.5mdrd2ωd
Solving for ωd gets 0.513 rad/s (as the magnitude), but this isn't the correct answer. What am I missing?