Calculating the angular momentum of rotating objects

In summary, calculating the angular momentum of rotating objects involves adding the individual angular momenta of infinitesimally small masses. However, this may not always result in an accurate answer as real objects have additional rotational motion about their center of mass. This can be represented by the sum of the angular momenta of the individual components of the object. To view the figures mentioned, it is recommended to use a newer version of Internet Explorer.
  • #1
YellowTaxi
196
0
Calculating the angular momentum of rotating objects.

When the angular momentum is computed you add all the individual angular momenta of infinitesimally small masses tilll you get the total, right ?

But doesn't that give a wrong answer - because each tiny piece of the object (rotating disk or whatever) is not just obiting the center, it's also spinning once on its own axis for every revolution of the disk.
So the total angular momentum of real objects will be higher than that for a bunch of particles circling a central axis but maintaining their orientation with no spin.

Do I have this right or am I all wrong ? ;-)
 
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  • #2
You have it wrong. The angular momentum of a real object (i.e., a non-point mass) is the angular momentum due to the linear momentum of the object's center of mass plus the rotational motion of the object about its center of mass:

[tex]\vec L_{\text{tot}} = m \vec r_{\text{cm}}\times \vec v_{\text{cm}} + \boldsymbol I \vec{\omega}[/tex]

This is equal to the sum of the angular momenta of the components of the object.
 
  • #3
Sorry, I can't see those figures on my computer, they just look like crazy squiggles on a black background and i can't make them out. Is there an easy way to see them in some other format or whatever ?

Thanks for the answer btw.
 
  • #4
You must be using a very old version of Internet Exploder.
 
  • #5
version 6
 

1. How is angular momentum defined?

Angular momentum is defined as the product of an object's moment of inertia and its angular velocity. It is a measure of the rotational motion of an object.

2. What is the equation for calculating angular momentum?

The equation for calculating angular momentum is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

3. How is angular momentum different from linear momentum?

Angular momentum is a measure of an object's rotational motion, while linear momentum is a measure of its linear motion. Angular momentum is a vector quantity and takes into account the direction of rotation, while linear momentum is a scalar quantity.

4. Can angular momentum change?

Yes, angular momentum can change. It can change when the object's angular velocity changes, or when its moment of inertia changes.

5. What are some real-world applications of calculating angular momentum?

Calculating angular momentum is important in understanding the motion of rotating objects, such as planets, satellites, and spinning tops. It is also crucial in engineering and designing machines that involve rotational motion, such as turbines and propellers.

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