Time given angular velocity/displacement

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SUMMARY

The discussion focuses on calculating the time taken for a gymnast to complete a tumbling maneuver while increasing her angular velocity from 2.90 rev/s to 5.40 rev/s over half a revolution. The initial angular velocity is converted to radians per second, resulting in 18.22 rad/s, while the final angular velocity is 33.92 rad/s. The correct formula used is θ = ωt, leading to a final calculation of time as approximately 0.12044 seconds after ensuring radians are used consistently.

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mcarloni
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A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 2.90 to 5.40 rev/s while rotating through one half of a revolution. How much time does this maneuver take?

Knowns:
w0 = 2.9 rev/sec * 2pi rad = 18.22 rad/sec
w = 5.4 rev/sec * 2pi rad = 33.92 rad/sec
θ = 180?

θ = 1/2 (w0 + w) t
180 = 1/2 (18.22 + 33.92) t
180 = 1/2 (52.14) t
(/180) 180 t = 26.07 (/180)
t = .1448

I know this is incorrect, and would appreciate help in the right direction.
 
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Don't mix radians and degrees!
 
Got it! :D

θ = 180 deg *(pi/180) = 3.14 rad

ω = 26.07

θ = ωt

which turns into

t = θ/ω

t = .12044
 

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