Angular velocity of a weighted rod left free to rotate around a pivot

[greg_rack]

Homework Statement

A rigid uniform rod of negligible mass is able to rotate around a pivot. Two masses, $m_1=250g$ and $m_2=200g$, are placed at the ends at distances $d_1=100cm$ and $d_2=150cm$ from the axis of rotation. The system, originally stable in its vertical position, gets moved slightly in the clockwise direction, putting it into rotation. Friction is negligible.
$\rightarrow$ what's the angular velocity of the system when it passes from its position of stable equilibrium?

Relevant Equations

Angular momentum

Hi guys,
I don't really know how to solve this problem.
The point is finding $\omega$ when $m_2$ passes from $m_1$'s original position.
Ideally, I'm thinking about some conservation of energy/momentum to apply here, but I'm quite confused.
Any hint?

 

[hacivat]

Begin by calculating where the center of mass is. Is it above or below the axis of rotation. That will give you a clue about (stable-unstable) equilibrium

 

[haruspex]

some conservation of energy/momentum

Yes, you have three to choose from: energy, linear momentum and angular momentum. Which will be conserved for the rod and masses system in this situation?

That will give you a clue about (stable-unstable) equilibrium

It is not really a question about equilibrium, stable or otherwise. In fact the question is stated incorrectly. The initial position is one of unstable equilibrium.

 

[hacivat]

It is not really a question about equilibrium, stable or otherwise. In fact the question is stated incorrectly. The initial position is one of unstable equilibrium.

Sorry, new to forum. Are we supposed to tell the answer or guide the way in this section?

 

[haruspex]

Sorry, new to forum. Are we supposed to tell the answer or guide the way in this section?

Point out errors, correct misunderstandings, offer hints.
But my comment to you was not to do with forum rules. Rather, I felt your post might lead Greg in a wrong direction.

 

[kuruman]

Homework Statement:: A rigid uniform rod of negligible mass is able to rotate around a pivot. Two masses, $m_1=250g$ and $m_2=200g$, are placed at the ends at distances $d_1=100cm$ and $d_2=150cm$ from the axis of rotation. The system, originally stable in its vertical position, gets moved slightly in the clockwise direction, putting it into rotation. Friction is negligible.
$\rightarrow$ what's the angular velocity of the system when it passes from its position of stable equilibrium?
Relevant Equations:: Angular momentum

View attachment 278894
Hi guys,
I don't really know how to solve this problem.
The point is finding $\omega$ when $m_2$ passes from $m_1$'s original position.
Ideally, I'm thinking about some conservation of energy/momentum to apply here, but I'm quite confused.
Any hint?

Maybe you are new to the forum, but you are not new to physics. You should know by now what an equation looks like and "Angular momentum" is not it. You will find that if you make an honest effort towards answering the problem and explaining what's on your mind, people will be more eager to help you.

For example, you say you are thinking that some conservation principle might be applicable here and you mention energy and angular momentum. These are appropriate candidates. You are expected then to tell us what must be true for one or the other to be conserved, and your own ideas whether these conditions are met in this particular case. Furthermore, in the "relevant equations" space write actual equations that express energy and angular momentum conservation to serve as starting point for the ensuing discussion. There you go.

 

[hacivat]

Rather, I felt your post might lead Greg in a wrong direction.

I respectfully disagree. Instead of saying him that the question is incorrectly stated I am trying to make himself to figure it out why the first use of word "stable" is not well suited there. And only way to figure it out this is to calculate the position of center of mass (which he is going to need to work towards the answer)

The point is finding ω when m2 passes from m1's original position.

Be careful! d1 is not equal to d2.