Find ω, the angular frequency of oscillation of the object

In summary, the conversation discusses the use of moment of inertia of a rod in a physics problem, explaining that it is a measure of resistance to angular acceleration and can be calculated using the formula I=1/3ML^2 for a rod. The conversation also mentions the relationship between angular velocity (ω) and gravity (g) for a rod, and how to determine the value of d for a non-uniform rod.
  • #1
joelkato1605
19
2
Homework Statement
The first image is the question, and the second is the hint.
Relevant Equations
ω=sqrt(g/L)
I=1/3ML^2 ?
The hint says to use the moment of inertia of the rod, however i have not covered this on my course and I don't know what it is.
After googling moment of inertia of a rod I found that it is a quantity expressing a body's tendency to resist angular acceleration, and for a rod I=1/3ML^2.

So ω=sqrt(g/L) and the hint says ω=sqrt(2mgd/I), so how is 1/L=2md/I?
 

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  • #2
HI,

Where does the $$ \omega = \sqrt{{g\over L}\ }$$ come from ?
Is it the full answer or is it just a hint and are you supposed to edit the expression by adding a coefficient ?

The Hint1 is correct; you can check it here (bearing in mind that the mass of your object is ##2m##).

I find it hard to believe that the exercise is given if moment of inertia hasn't been covered.
 
  • #3
No sorry that's just what I typed as an initial guess but it was wrong.

Thanks that link was very helpful.

And the only time I have seen moment of inertia was in a example about stars rotating, and its value was just stated so I didn't know any formulas to find it.

So I=(2mL^2)/3, therefore I need to find what d equals, but it doesn't say the rod is uniform, so d= L*sqrt(2)/4, and then substitute and simplify.
 
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  • #4
I think you have it all nicely lined up ! And yes, you may take the rod as uniform.
Hope it works !
 
  • #5
Yeah it was correct, thanks for the help.
 
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1. What is angular frequency?

Angular frequency, denoted by the symbol ω, is a measure of the rate at which an object oscillates or rotates around a central point. It is measured in radians per second (rad/s).

2. How is angular frequency related to frequency and period?

Angular frequency is directly proportional to frequency and inversely proportional to period. This means that as the angular frequency increases, the frequency also increases, while the period decreases.

3. What factors affect the angular frequency of an object?

The angular frequency of an object is affected by its mass, the force acting on it, and the distance from the central point of rotation. It is also influenced by the type of oscillation or rotation, such as simple harmonic motion or circular motion.

4. How is angular frequency calculated?

The angular frequency can be calculated using the formula ω = 2πf, where f is the frequency in hertz (Hz). It can also be calculated using the formula ω = 2π/T, where T is the period in seconds (s).

5. Why is angular frequency important in physics?

Angular frequency is an important concept in physics because it is used to describe the motion of objects in circular or oscillatory motion. It is also used in the study of waves and vibrations, as well as in various engineering applications such as in the design of rotating machinery.

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