Question

Propeller blades in aeroplane are $2m$ long
(a) When propeller is rotating at $1800rev/min$, compute the tangential velocity of tip of the blade.
(b) What is the tangential velocity at a point on blade midway between tip and axis?

Answer 1

Radius, $r=2$ $m$

$\left(a\right)$ Angular velocity, $\omega =1800$ $rev/min$

$⟹\omega =\frac{1800}{60}$ $rev/s$

$⟹\omega =30$ $rev/s$

$⟹\omega =30\times 2\pi$ $rad/s$

$⟹\omega =60\pi$ $rad/s$

Tangential velocity, $V=r\omega$

$⟹V=2\times 60\pi$

$⟹V=120\pi$

$⟹V=377$ $m/s$

$\left(b\right)$ Tangential velocity at a point on blade midway between tip and axis:

$V=\frac{r}{2}\times \omega$

$⟹V=1\times 60\pi$

$⟹V=60\pi$

$⟹V=188.49$ $m/s$