Find ω, the angular frequency of oscillation of the object

[joelkato1605]

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?

 

[BvU]

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.

 

[joelkato1605]

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.

 

[BvU]

I think you have it all nicely lined up ! And yes, you may take the rod as uniform.
Hope it works !

 

[joelkato1605]

Yeah it was correct, thanks for the help.