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  4. The wheel in figure has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s. You want to shoot a 20-cm-long arrow parallel to this axle and through the wheel <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/0791b3d3211f2c41b9a6f3cbe7771b91-.png />

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Q. The wheel in figure has eight equally spaced spokes and a radius of $30\, cm$. It is mounted on a fixed axle and is spinning at $2.5 \,rev/s$. You want to shoot a $20-cm$-long arrow parallel to this axle and through the wheel
image

System of Particles and Rotational Motion

Solution:

To avoid touching the spokes, the arrow must go through the wheel in not more than
$\Delta t =\frac{1 /8 \,reV}{2.5 \, reV / s} =0.050 \,s $
The minimum speed o the arrow is then
$v_{min} =\frac{20\,cm}{0.050\,s} =400\, cm /s =4.0 \, m /s$