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Angular velocity proportion

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fermat7

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Hey ...

my question is to find a relationship between two angular velocities in this configuration.

i get a proof for the first one one, but i am not quiet sure about it. i need your answer to

check the way i do it. because i started from the fact that the speed of the center of the

rolling object expressed in the two referentials.

thanks for your time)

best regards.
 

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