How Is Proton Magnetic Moment Linked to Its Rotational Motion?

In summary, angular momentum is a measure of an object's rotational motion, calculated by multiplying its moment of inertia with its angular velocity. It differs from linear momentum, which only takes into account an object's linear motion. Spin is a type of angular momentum that is intrinsic to particles and is related to the Pauli exclusion principle. Both angular momentum and spin can be changed through interactions, but the total angular momentum and spin of a closed system remain constant due to the law of conservation of angular momentum.
  • #1
Stellar1
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Homework Statement


Assume that the proton magnetic moment is to be interpreted as due to the rotational motion of a positive spherical uniform charge distribution of radius R spinning about its axis with angular speed w. Using classical relationship between the angular momentum and rotational speed show that:

wR^2 =5s/2m


2. The attempt at a solution

l = R*m*v = R*m*R*w = m*w*R^2

wR^2 = l/m

How is l related to 5s/2?
 
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  • #2
I=2/5 mr^2 for a sphere and
L=Iw by definition so you can finish/restart the problem now...
 

1. What is angular momentum?

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

2. How is angular momentum different from linear momentum?

While linear momentum is the product of an object's mass and linear velocity, angular momentum takes into account an object's rotation around an axis. Linear momentum is a vector quantity, while angular momentum is a vector quantity.

3. What is spin in relation to angular momentum?

Spin is a type of angular momentum that is intrinsic to particles, such as electrons and protons. It is a quantized property that determines the orientation of a particle's intrinsic angular momentum.

4. How is spin related to the Pauli exclusion principle?

The Pauli exclusion principle states that no two particles can have the same set of quantum numbers. Spin is one of these quantum numbers, and it can only take on two values: spin up or spin down. This principle is essential in understanding the behavior of electrons in atoms.

5. Can angular momentum and spin be changed?

Yes, angular momentum and spin can be changed through interactions with other particles or fields. For example, when an electron is excited to a higher energy level in an atom, its angular momentum and spin may change. However, the total angular momentum and spin of a closed system remain constant, in accordance with the law of conservation of angular momentum.

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