Question

A basket ball of radius R is spun with an angular speed $\overrightarrow{\omega }=\omega \hat{k}$ and its CM moves with a speed v. The aerodynamic lift experienced by the ball is$F=x\pi \rho R^{3}v\omega$ . Assume $\rho =$ density of air. Find the value of x.

Answer 1

Aerodynamic lift experienced by the lift will be $F=\Delta P\times A_{effec}$ where $A_{effec}=\pi R^2$

Neglecting difference in potential energy due to gravity

$\Delta P=\frac{1}{2}\rho [(v+R\omega {)}^2-(v-R{\omega }^2)]$

$\Delta P=\frac{1}{2}\rho \left(4vR\omega \right)=2vR\rho \omega$

Hence, $F=2\pi R^{3}v\rho \omega$

So ,$x=2$