Question

Consider a rigid square plate of 1m side, its left edge being attached to a torsional spring of stiffness 10Nm/rad. There is an air flow coming from the right. The equilibrium position of the plate without flow is the horizontal position, as represented on the figure. At which velocity (m/s) does the static instability occur?

Answer 1

Here, we have given density of air as 1.225 $\frac{kg}{m^3}$ , Torsional stifness= 10 Nm/rad

Here figure attached to this question is below

So here ,

Net torque= Force*perpendicular distance

Torsional stiffness$\times angle=\rho A v^2 \times side$

$10\times 10 \times \frac{\pi}{180}=1.225 \times 1\times v^2 \times0.5$

v=1.687 m/s is the velocity of air