Solve Rotation Problem: Wheel w/ 8 Spokes & 30cm Radius

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SUMMARY

The problem involves calculating the minimum speed required for a 26-cm-long arrow to pass through a wheel with eight spokes, each spaced 45 degrees apart, while the wheel spins at 3.6 revolutions per second. The angular velocity of the wheel is determined to be 7.2π radians per second. The time available for the arrow to travel through the gap between spokes is calculated to be approximately 0.03472 seconds. Consequently, the minimum speed of the arrow must be at least 750 cm/s to avoid hitting any spokes.

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Homework Statement


The wheel in Fig. 10-29 has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 3.6 rev/s. You want to shoot a 26-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have?
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Homework Equations




The Attempt at a Solution


Okay so first i wrote down my givens.
I found the angle between the spokes to be 45 or pi/4 radians.

I did the 3.6rev/s time 2pi rad/rev which equals 7.2pi radians/s. That would be the angular velocity.
I did pi/4 radians divided by 7.2 pi radians/s which equals 0.03472s for time.
Now, I'm kinda stuck.
Any help would be grateful. Thankyou!
 
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You should see that the arrow only has 0.034s to travel 26 cm...
 
heh.. i feel kinda stupid now...

thank you for the help agh.. it was so obvious i didn't see it >.<
 

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