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.