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Equations of motion in a rotatin frame

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A student is performing measurements with a hockey puck on a large merry-go-round with a frictionless, horizontal, flat surface end has a constant angular velocity of W(bar) and rotates counter clockwise as seen from above.

Given: the radius of the merry-go-round is R= 1m, W(bar)=1 radian/sec.

Initial position is: x=-.5R, y=0 and the initial direction of Vo is in the +y direction

inital velocities Vo (m/s):

a)1.5, b).8 c).45 d)..328

i) find the effective force on the puck after it is given a push in the y direction

ii) Plot the path for the various initial velocities a - d above

Please show all math including equations and matrices.

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Solution Summary

The 9 pages document contains a complete solution of the puck on the merry-go-round problem, includig a full solution of teh coupled equations of motion using eigenvalues and eigenvectors.

Solution Preview

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We define the coordinate, velocity and angular velocity vectors as:

The centrifugal acceleration is defined as:

While the Coriolis acceleration is:

Thus, the equations of motion in the merry-go-round system are:

To solve these coupled equations, we decouple them by defining:

...

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