Parallel Axis Thereom to find angular velocity

[Sepamo]

Homework Statement

A meter stick is freely pivoted about a horizontal axis at the 94.7 cm mark. Find the (angular) frequency of small oscillations, in rad/s

Homework Equations

I=Icm+md^2
$\Sigma$ $\tau$=I $\alpha$
mg*sin($\Theta$)=-I(d^2$\Theta$/dt^2)

The Attempt at a Solution

5.37 rad/s

 

[antny]

Hi,

The torque equation you wrote should be: -mgd*sin$\theta$=Id^2$\theta$/dt^2
(you forgot the 'd' on the left-side.)

For small angles, sin$\theta$$\approx$$\theta$

The torque equation can then be rewritten as:

-(mgd*$\theta$)/I=d^2$\theta$/dt^2

This is a common differential equation that arises in physics, and it describes a type of oscillatory motion known as "simple harmonic motion".

The period is:

T=2$\pi$*$\sqrt{I/mgd}$

The angular frequency can be easily found from here.