The wheel in the figure below has eight equally spaced spokes and a radius of 30

Question

The wheel in the figure below has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.1 rev/s. You want to shoot a 14 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? m/s Does it mater where between the axle and rim of the wheel you aim? Yes no If so, where is the best location? Outside the rim close to the axle close to the rim doesn't matter

Explanation / Answer

We don't even need the radius!

Since there are 8 evenly spaced spokes, one spoke will pass through a given point every eighth of a revolution.

So the minimum speed the arrow must travel is the speed that allows it to pass completely through the wheel (i.e. travel a distance equal to the length of the arrow, 14.0 cm) in the time it takes the wheel to complete 1/8 of a revolution.

But how long does it take to complete 1/8 of a revolution? Well, it completes 2.1 revolutions per second so it takes 1/2.1 seconds per revolution and divide by 8 to take the time taken to complete 1/8 of a revolution.

So the time taken to complete 1/8 of a revolution is 1/(8*2.1) = 0.059523 seconds.

And remember speed is distance divided by time. Distance = 14.0 cm, time we have just found. So the speed is (14.0 cm)/(0.059523 s) = 235.20cm/s = 2.35 m/s.

b) the spokes and arrow thickness are ignored, then the radius is not a facto

outside of the rim

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