Calculating Angular Momentum of a Rotating Rod | Mass M, Angular Velocity ш

In summary, the conversation discusses the calculation of the angular momentum of a rod rotating about one end and its center of mass. The formula for calculating the angular momentum of a rod is provided, along with links to resources for more information. The concept of finding the angular momentum about a point is also discussed, with the conclusion that the angular momentum about the center of mass is equivalent to the angular momentum in a reference frame where the center of mass stays at the origin. The importance of putting in effort and showing work in problem solving is emphasized.
  • #1
kuyt
8
0
What is the angular momentum of a rod rotating about one end (mass M and angular velocity ш),about its center of mass?
 
Physics news on Phys.org
  • #2
kuyt said:
What is the angular momentum of a rod rotating about one end (mass M and angular velocity ш),about its center of mass?
Is the rod rotating about one end or its center of mass?
 
  • #3
about one end
 
  • #5
But this is something fundamental,calculating angular momentum of a system about arbitary points in space.:confused:
 
  • #6
In the second link the 'bubbles' are hot links.
Navigate through "Mechanics", then "Rotation", then "Moment of Inertia".
Click on "Common Forms" for Enlightenment!
 
  • #7
Find the angular momentum of a differential length (dm*v*r) and integrate from r=0 to L.
 
  • #8
kuyt said:
But this is something fundamental,calculating angular momentum of a system about arbitary points in space.:confused:
Yes, it is, and you can answer it by calculating the angular momentum of individual point about the end of the rod, then integrating them along the length of the rod. The result of doing that would be the formula at http://scienceworld.wolfram.com/physics/MomentofInertiaRod.html
that you could get to following the links you were given in tadchem's response.
 
  • #9
HallsofIvy said:
Yes, it is, and you can answer it by calculating the angular momentum of individual point about the end of the rod, then integrating them along the length of the rod. The result of doing that would be the formula at http://scienceworld.wolfram.com/physics/MomentofInertiaRod.html
that you could get to following the links you were given in tadchem's response.

it gives moment of inertia not angular momentum! Can we use the general formula(if its correct):angular moment abt any point=angular moment of a fictitious particle (of mass m at the position of COM)abt that point + angular moment of the body abt com ?
 
  • #10
hello kuyt, i think you should have a look at the angular momentum equation ie., L= r X P and v=rw. So, use r=l/2 where l=length of rod. hope that makes sense..
 
  • #11
No,it not that easy I guess.
P.S can anyone giveme the final answer(in terms of angular velocity,mass and length)and ofcourse the explanation,instead of links
 
  • #12
It's (1/3)wmL^2 for angular speed w.
 
  • #13
^but that about one of the ends ,not com
 
  • #14
Ah, so you're trying to find the angular momentum about the com, in a system where the rod is rotating about one end.
 
  • #15
yes :approve:
 
  • #16
hmm. Tricky one. Well, I'm pretty sure that the whole point of saying the angular momentum "about a point" is equivalent to calculating the angular momentum, given that the origin is the point about which we want to find the angular momentum.

So I think the angular momentum about the COM is simply angular momentum, given that our origin is the COM. And in our original reference frame, the rod was rotating around the end. So in a reference frame where the COM stays at the origin, the angular momentum will simply be
[tex] \omega \frac{mL^2}{12} [/tex]
(in other words, same as what the angular momentum would be for a system where the rod is rotating around it's COM.)
 
  • #17
The links provide helpful information.

Students are expected to demonstrate effort and show their work. We do not spoon feed students with answers.
 

1. How do I calculate the angular momentum of a rotating rod with given mass and angular velocity?

To calculate the angular momentum of a rotating rod, you can use the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia can be calculated using the formula I = 1/12mL^2, where m is the mass of the rod and L is the length of the rod.

2. What is the unit of measurement for angular momentum?

The unit of measurement for angular momentum is kilogram meters squared per second (kg·m^2/s).

3. How does the mass of the rod affect its angular momentum?

The mass of the rod directly affects its angular momentum. The higher the mass, the greater the angular momentum, assuming the angular velocity remains constant.

4. What happens to the angular momentum if the angular velocity increases?

If the angular velocity increases, the angular momentum also increases. This is because angular momentum is directly proportional to angular velocity.

5. Can the angular momentum of a rotating rod be negative?

Yes, the angular momentum of a rotating rod can be negative. This occurs when the direction of the angular momentum is opposite to the direction of rotation. This can happen if the rod is rotating in a clockwise direction, while the angular momentum is calculated in a counterclockwise direction.

Similar threads

Replies
1
Views
291
Replies
3
Views
1K
Replies
5
Views
951
Replies
19
Views
1K
Replies
1
Views
408
Replies
15
Views
905
  • Mechanics
Replies
9
Views
1K
Replies
36
Views
3K
Back
Top