Similarly to how the equation for the lift force ($F_L$) was derived using the density ($\rho$), the coefficient of lift ($C_L$), the surface that generates lift ($S_w$), and the speed with respect to the medium ($v$)

$ F_L =\displaystyle\frac{1}{2} \rho S_w C_L v ^2$

in this analogy, what corresponds to the surface that generates lift ($S_w$) will be equivalent to the total object profile ($S_p$) and the coefficient of lift ($C_L$) to the coefficient of resistance ($C_W$), thus the resistance force ($F_W$) is calculated:

$ F_W =\displaystyle\frac{1}{2} \rho S_p C_W v ^2$

The drag coefficient is measured and, in turbulent flows over aerodynamic bodies, values are generally found around 0.4.

(ID 4418)

Given that the the kinetic energy of rotation ($K_r$) of the physical pendulum, in terms of the moment of inertia for axis that does not pass through the CM ($I$) and the angular Speed ($\omega$), is represented by:

$ K_r =\displaystyle\frac{1}{2} I \omega ^2$

and that the potential Energy Pendulum ($V$), as a function of the gravitational mass ($m_g$), the pendulum Length ($L$), the swing angle ($\theta$) and the gravitational Acceleration ($g$), is expressed as:

$ V =\displaystyle\frac{1}{2} m_g g L \theta ^2$

The total energy equation is written as:

$E = \displaystyle\frac{1}{2}I\omega^2 + \displaystyle\frac{1}{2}mgl\theta^2$

Knowing that the period ($T$) is defined as:

$T = 2\pi\sqrt{\displaystyle\frac{I}{mgl}}$

We can determine the angular frequency as:

$ \omega_0 ^2=\displaystyle\frac{ m g L }{ I }$

(ID 4517)

(ID 12870)

(ID 12876)

(ID 12877)