What are the equations for angular momentum?

In summary, angular momentum is a measure of an object's rotation around a fixed point. Objects can become stuck in angular momentum when there is no external torque to change their rotational speed or direction. This can be seen in real-life examples such as spinning tops and the Earth's rotation. To break out of angular momentum, an external torque must be applied. Being stuck in angular momentum can have both positive and negative implications, providing stability but also making it challenging to change an object's motion.
  • #1
AdrianMay
121
4
Hi folks,

The attachment is from Sakurai where he's getting started on angular momentum. I don't understand how he gets between the two equations I stuck a ? on. Any hints gratefully appreciated.

Adrian.
 

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  • #2
Hi Adrian! :smile:

It's ordinary algebra …

A(pq + rs)B = ApqB + ArsB,

together with Sz|+> = |+>, Sz|-> = -|->, and the expansion definition of exp :wink:
 
  • #3
I swear the exact same question was on this forum or the HW:Advanced Physics 2 weeks ago.
 

FAQ: What are the equations for angular momentum?

What is angular momentum and why do objects get stuck in it?

Angular momentum is a measure of the rotation of an object around a fixed point. Objects can get stuck in angular momentum when there is no external torque acting on them to change their rotational speed or direction. This can occur when there is a balance of forces or when the object is in a state of equilibrium.

How does angular momentum affect objects in space?

In space, objects can become stuck in angular momentum due to the lack of friction and external forces. This can cause objects to continue rotating at a constant speed and direction, making it difficult to change their trajectory or orientation.

What are some real-life examples of objects getting stuck in angular momentum?

One common example is a spinning top or gyroscope. These objects rely on their angular momentum to maintain their balance and keep them spinning. Another example is the Earth's rotation, which is a result of its angular momentum and keeps it in a constant orbit around the sun.

How can objects break out of being stuck in angular momentum?

In order for an object to break out of angular momentum, an external torque must be applied to change its rotational speed or direction. This can be achieved through the use of forces such as friction, gravity, or a push or pull from another object.

What are the implications of being stuck in angular momentum?

Being stuck in angular momentum can have both positive and negative implications. On one hand, it can provide stability and balance to objects, such as in the case of a spinning top. However, it can also make it difficult to change an object's motion or trajectory, which can be problematic in certain situations, such as trying to maneuver a spacecraft in space.

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