Moment of inertia of a charged spinning top

In summary, the moment of inertia of a spinning top with charge Q submerged in an electromagnetic field is not affected by the electric field. The moment of inertia is a product of an object's mass and dimensions and is not influenced by motion or external forces such as friction. The dipolar moment generated by the electric field may affect the top's rotation, but the moment of inertia remains constant.
  • #1
JCOM44
How can I calculate the moment of inertia of a spinning top with charge Q submerged in an electromagnetic field?

I've already calculated it for the case with no charge, but I don't know how to do this.
 
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  • #2
I'm not aware of any context where charge has anything to do with the moment of inertia.
 
  • #3
But the electric field generates a dipolar moment, which makes the spinning top rotate different affecting the moment of inertia, isn't that right?
 
  • #4
That sounds to me like an object with a particular moment of inertia, based only on the location of it's mass, reacting to a force from the electric field. The moment of inertia is not a function of the force field.
 
  • #5
JCOM44 said:
isn't that right

No.

The moment of inertia is the same. The forces and torques on the top could be different, but the moment of inertia is the same.
 
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  • #6
Can't I consider the dipolar moment as an electromagnetic analogue of the moment of inertia?
 
  • #7
I don't know what good that will do.
 
  • #8
Then would you say that when we have a charged spinning top with a defined moment of inertia and it is suddenly exposed to an electromagnetic field, the way it rotates won't change?
 
  • #9
If the field applies a force or torque to the top, it's motion will change. But it's moment of inertia will not.
 
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  • #10
Maybe it will help if I put it this way: would anything change if you put a (charged) ballerina in an electromagnetic field to execute her fouettes?



Ballerina's would make excellent physicists.
 
  • #11
An object's moment of inertia is merely the extent to which it resists rotational acceleration about a particular axis. It's a product of the object's mass and dimensions, it actually has nothing to do with motion.

Take the moment of inertia of a solid sphere for example, which can be expressed as
$$I=\frac{2}{5}mr^2$$
As you can see, motion doesn't play a part whatsoever (we're talking classically here).
 
  • #12
Even a force like friction doesn't change the moment of inertia.

Perhaps the OP is confusing momentum and moment of inertia?
 

1. What is the moment of inertia of a charged spinning top?

The moment of inertia of a charged spinning top refers to the resistance of the top to changes in its rotational motion. It is a measure of the distribution of mass around the axis of rotation and depends on the shape and size of the top.

2. How is the moment of inertia of a charged spinning top calculated?

The moment of inertia can be calculated by multiplying the mass of the top by the square of its distance from the axis of rotation. In the case of a charged spinning top, the moment of inertia also takes into account the charge and its distance from the axis of rotation.

3. How does the charge affect the moment of inertia of a spinning top?

The charge on a spinning top can affect its moment of inertia by changing the distribution of mass around the axis of rotation. This is because the charge will exert a force on the magnetic field, causing the top to resist changes in its rotational motion.

4. Are there any real-life applications of the moment of inertia of a charged spinning top?

Yes, the moment of inertia of a charged spinning top is important in the study of gyroscopic motion. It is also relevant in the development of technologies such as gyroscopes, which are used in navigation systems, satellites, and other devices that require stable rotational motion.

5. Can the moment of inertia of a charged spinning top be changed?

Yes, the moment of inertia of a charged spinning top can be changed by altering its shape, mass distribution, or charge. This can be done through physical manipulation or by changing the properties of the materials used to make the top.

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