- #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.

L

_{t}=r

_{t}p

_{s}=L

_{t}=r

_{t}m

_{s}v

_{t}

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.

L

_{d}=I

_{d}ω

_{d}=0.5m

_{d}r

_{d}

^{2}ω

_{d}

L

_{d}+L

_{t}=0

Setting them equal to each other gets:

r

_{t}m

_{t}v

_{t}=0.5m

_{d}r

_{d}

^{2}ω

_{d}

Solving for ω

_{d}gets 0.513 rad/s (as the magnitude), but this isn't the correct answer. What am I missing?