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Parallel Axis Thereom to find angular velocity

by Sepamo
Tags: meter stick, oscillation
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Sepamo
#1
Jul21-11, 10:58 PM
P: 4
1. The problem statement, all variables and given/known data
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


2. Relevant equations
I=Icm+md^2
[itex]\Sigma[/itex] [itex]\tau[/itex]=I [itex]\alpha[/itex]
mg*sin([itex]\Theta[/itex])=-I(d^2[itex]\Theta[/itex]/dt^2)
3. The attempt at a solution
5.37 rad/s
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antny
#2
Jul24-11, 07:41 PM
P: 6
Hi,

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

For small angles, sin[itex]\theta[/itex][itex]\approx[/itex][itex]\theta[/itex]

The torque equation can then be rewritten as:

-(mgd*[itex]\theta[/itex])/I=d^2[itex]\theta[/itex]/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[itex]\pi[/itex]*[itex]\sqrt{I/mgd}[/itex]

The angular frequency can be easily found from here.


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