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

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The problem involves a wheel with eight spokes, a radius of 30 cm, and an angular velocity of 7.2π radians/s. To avoid hitting the spokes, the arrow, which is 26 cm long, must travel through the wheel in a calculated time of 0.03472 seconds. The discussion highlights the need to determine the minimum speed required for the arrow to successfully pass through the wheel without contact. The user expresses frustration at initially overlooking the straightforward nature of the solution. The key takeaway is the importance of calculating both the angular velocity and the time constraint for the arrow's travel.
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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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