Angular momentum in general motion

In summary, the conversation discusses the general motion of a rigid body and the equation L = Σmiri × vi. The speaker points out that terms 3 and 4 in the equation are zero in the centre of mass frame, but term 4 is not. They mention that term 2 and 3 are also zero in the equation. The speaker is unsure of what they are missing and asks for clarification.
  • #1
aim1732
430
2
For general motion of a rigid body :
[Vectors in bold]
L = Σ miri × vi
= Σ mi(r0+ri,cm)×(vo+vi,cm)
= Σmir0×vo + Σr0×(mivi,cm) + Σ(miri,cmvo + Σmiri,cm×vi,cm ...[1]
If the centre of coordinate system is at the centre of mass then by definition of centre of mass: Σmiri=0 and Σmivi,cm=0.
Now here's the the problem: terms 3 and 4 in [1] are zero in the centre of mass frame but the term 4 is not.But then using the same arguments I can say it is zero too. I am missing a point but can not point out what.
 
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  • #2
I'm sure you mean term 2 and 3 are zero in [1].
Term 4 is not zero because you have to sum over both, r and v simultaneously.
 
  • #3
Heck that was easy.Thank you very much!
 

Related to Angular momentum in general motion

1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object around a fixed point. It is the product of an object's mass, its velocity, and its distance from the fixed point.

2. How is angular momentum different from linear momentum?

Angular momentum involves the motion of an object around a fixed point, while linear momentum involves the motion of an object in a straight line. Angular momentum is also a vector quantity, meaning it has both magnitude and direction, while linear momentum is a scalar quantity.

3. How is angular momentum conserved?

In general motion, angular momentum is conserved when there is no external torque acting on the system. This means that the total angular momentum before and after an event or interaction remains the same.

4. 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. Moment of inertia is a measure of an object's resistance to rotational motion.

5. How is angular momentum used in real-world applications?

Angular momentum is used in many real-world applications, such as in the design of vehicles and machines that rotate, in the study of celestial bodies and their orbits, and in sports such as figure skating and gymnastics. It is also an important concept in quantum mechanics and the behavior of subatomic particles.

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