Question

calculate the angular frequency of hinged rigid body.

Answer 1

Oscillations of hinged rigid body are described by the model of physical pendulum.

For mathematical pendulum $\displaystyle T = 2 \pi \sqrt{\frac{L}{g}}$ where L is a length of pendulum.

For physical pendulum we can introduce equivalent length L - the distance from the pivot to the centre of oscillation.

$\displaystyle L = \frac{I}{mR}$

where where I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the centre of the mass.

So, $\displaystyle T = 2\pi \sqrt{\frac{I}{mgR}}$ .

Angular frequency $\displaystyle \omega = \frac{2\pi}{T} =\sqrt{ \frac{mgR}{I}}$ .