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 $v$. Find the aerodynamic lift experienced by the ball. Assume $\rho =$density of air.

Answer 1

$\overrightarrow{\omega }=\overrightarrow{\omega }\hat{R}$

Neglecting difference in potential energy due to gravity

$\Rightarrow \frac{1}{2}\rho {\left(v_b\right)}^2-\frac{1}{2}\rho {\left(v_t\right)}^2=△P$

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

$△P=\frac{1}{2}\rho (v^2+R^2{\omega }^2-2rR\omega -r^2-R^2{\omega }^2+2rR\omega )$

$△P=2rR\omega \rho$

Aerodynamic lift$=2rR\omega \rho \times \pi R^2$

$=2R^{3}r\omega \rho$