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## Homework Statement

A wheel has six spokes of length 30 cm. The wheel is rotating with an angular velocity of 2.5 rotation per second. We want to throw an arrow, of length 24 cm, through the wheel. What is the minimal velocity required for the arrow to go through the wheel without touching the spokes.

## Homework Equations

v = s / t

[tex]\omega[/tex] = [tex]\theta [/tex] / t

## The Attempt at a Solution

The times for the arrow to go through have to be equal the time one spoke goes around 1/6 of the wheel.

so the system: v = s/t and [tex]\omega[/tex] = [tex]\theta [/tex] / t

gives: v = ([tex]\omega[/tex] / [tex]\theta [/tex]) * s

[tex]\omega[/tex] = 2.5 rotation per second * 360degree = 900 degree/s

[tex]\theta [/tex] = 360 degree / 6 = 60 degree

v = ([tex]\omega[/tex] / [tex]\theta [/tex]) * s = (900 degree/s / 60 degree) * 24 cm = 360 cm

is this right?