At t=0 the angular velocity of the mass is and the string breaks. For later times a force acts which keeps the angular velocity constant at . The force has no radial component, i.e., . Find .
First, write Newton’s second law:
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(0.1) |
But, so
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(0.2) |
The first equation is easily solved:
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(0.3) |
and so
|
(0.4) |
where a and b are constants to be determined. Since and , it is easy to show that . Therefore
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(0.5) |
Since ,
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(0.6) |
Finally, from the equation (0.2) for F,
. |
(0.7) |
Early trajectory of m for R0=1
Trajectory of m for R0=1 over 3600 (note log scale for r)