Question

A wheel of radius 0.4 m is stuck in wet mud. It picks up the dirt and flings it all over as it rotates. The wheel rotates with an angular velocity $omega$ and a dirt particle files off from the top pf the wheel. It lands 4 m from the base of the wheel where it was picked up. What is the angular velocity of the wheel?

Answer 1

$x=vt$

and $y=\frac{1}{2}g{t}^2=2r$

$⟹t=\sqrt{\frac{4r}{g}}$

$⟹v=\frac{x}{t}=x\sqrt{\frac{g}{4r}}$

$⟹\omega =\frac{v}{r}=\frac{x}{r}\sqrt{\frac{g}{4r}}$

$⟹\omega =\frac{4}{0.4}\sqrt{\frac{10}{1.6}}$

$⟹\omega =25rad/s$