Understanding Angular Momentum in Rigid Body Rotation

AI Thread Summary
Angular momentum for a rigid body can be expressed as the product of its moment of inertia and angular velocity only when rotating about an axis of symmetry, as the moment of inertia is a tensor that simplifies in this case. When rotation occurs around a non-symmetry axis, the angular momentum does not align with the rotation axis due to the tensor's non-diagonal nature. This concept is often covered in mechanics textbooks, but explanations can be lacking for high school students. An example illustrating this phenomenon could clarify the relationship between angular momentum and rotation axes. Understanding these principles is crucial for grasping the complexities of rigid body dynamics.
mr.physics
Messages
21
Reaction score
0
Why can only the angular momentum of a rigid body rotating about an axis of symmetry be expressed as the product of the body's moment of inertia and its angular velocity?
 
Physics news on Phys.org
The "moment of inertia" is actually a tensor. If a body is rotated about an axis that is not a symmetry axis (or, more generally, an axis for which the tensor is not diagonal), the angular momentum in not in the direction of the axis of rotation.
This is discussed in Mechanics terxtbooks.
 
Hmm.
I still don't really understand why not and my textbook doesn't supply much of an explanation.
Could someone please explain more thoroughly in terms a high school physics student might be privy to?
 
clem said:
If a body is rotated about an axis that is not a symmetry axis [..] the angular momentum [is] not in the direction of the axis of rotation.
Would you describe (or cite) an example of that?
 

Thread 'Is calling fictitious forces not real just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

I Effects of External Torques on the Angular Momentum of Asymmetric Bodies
Replies
3
Views
2K
I Conservation of Angular Momentum vs a gyro at the North Pole
Replies
16
Views
1K
I Moment of Inertia about an axis and Torque about a point
Replies
5
Views
3K
I Is angular momentum perpendicular to fixed axis of rotation constant?
Replies
1
Views
1K
Is angular momentum taken about a point or an axis?
Replies
17
Views
2K
Torque, angular momentum and a fixed axis-of-symmetry requirement
Replies
1
Views
1K
I Conservation of angular momentum -- spinning a bicycle wheel in space
Replies
2
Views
2K
Rotation: inertial frame vs. body-fixed frame
Replies
12
Views
4K
I Conservation of angular momentum during collisions
Replies
3
Views
3K
B Why does torque increase with increasing moment of inertia?
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top