- #1

MatinSAR

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- 182

- Homework Statement
- Please see below.

- Relevant Equations
- ##L_i= \sum_j I_{ij} \omega_{j}##

Hello. I am reading Classical dynamics of particles and systems(Book by Stephen Thornton), I have problem in understanding the coordinate system they choose to define angular momentum for a rigid body. At the beginning of the chapter 11 they say:

They use 2 coordinate systems to describe motion of a rigid body. One is the fixed coordinate system. In this system we can use Newton's law of motion without any problem. The second coordinate system is fixed with respect to the body. In the inertial reference frame, the rigid body and the second coordinate system move in sync, causing them to remain stationary relative to each other. So if a rigid body consist of ##n## particles with mass of ##m_{\alpha}## in this system the particle ##\alpha## doesn't move. I can say that it doesn't have momentum in this system because it is fixed with respect to it.

Following that, they demonstrate the process of deriving an equation for the kinetic energy of a rigid body.

If we make the origin of the body corrdinate system coinside with center of mass of the body, it results in:

Up to this point, everything is clear. The issue arises in the next section, where they introduce the definition of angular momentum for a rigid body.

I cannot understand this. If point O is fixed in the body coordinate system, it could be any point on the body because the body doesn't move in the body coordinate system. Therefore, the angular momentum of this rigid body with respect to a fixed point in the body coordinate system should be 0! I believe the angular momentum should be defined with respect to the fixed coordinate system rather than a fixed point in the body coordinate system. Am I wrong?

Any help would be appreciated.

Edit 1: I edited a typo.

They use 2 coordinate systems to describe motion of a rigid body. One is the fixed coordinate system. In this system we can use Newton's law of motion without any problem. The second coordinate system is fixed with respect to the body. In the inertial reference frame, the rigid body and the second coordinate system move in sync, causing them to remain stationary relative to each other. So if a rigid body consist of ##n## particles with mass of ##m_{\alpha}## in this system the particle ##\alpha## doesn't move. I can say that it doesn't have momentum in this system because it is fixed with respect to it.

Following that, they demonstrate the process of deriving an equation for the kinetic energy of a rigid body.

If we make the origin of the body corrdinate system coinside with center of mass of the body, it results in:

Up to this point, everything is clear. The issue arises in the next section, where they introduce the definition of angular momentum for a rigid body.

I cannot understand this. If point O is fixed in the body coordinate system, it could be any point on the body because the body doesn't move in the body coordinate system. Therefore, the angular momentum of this rigid body with respect to a fixed point in the body coordinate system should be 0! I believe the angular momentum should be defined with respect to the fixed coordinate system rather than a fixed point in the body coordinate system. Am I wrong?

Any help would be appreciated.

Edit 1: I edited a typo.

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