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Parallel Axis Thereom to find angular velocity

by Sepamo
Tags: meter stick, oscillation
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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
[itex]\Sigma[/itex] [itex]\tau[/itex]=I [itex]\alpha[/itex]
3. The attempt at a solution
5.37 rad/s
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Jul24-11, 07:41 PM
P: 6

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:


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:


The angular frequency can be easily found from here.

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