Rotational Inertia of compass needle

In summary, the problem involves a compass needle in a uniform magnetic field, oscillating with a frequency of 5 Hz and requiring a millijoule of work to twist it 180º. The question is asking for the rotational inertia of the needle, and the solution may involve equations related to frequency and work/energy in a magnetic field.
  • #1
olyviab
11
0

Homework Statement



A small compass needle is situated in a uniform magnetic field. When displaced from its stable equilibrium position through a small angle and then released, it oscillates with a frequency of 5 Hz. A millijoule of work is needed to twist the compass needle round through 180º, so that its magnetic moment is in the opposite direction to the magnetic field. What is the rotational inertia of the needle?


2. The attempt at a solution

I don't understand how to start this problem any help would be great.
 
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  • #2
What equations have you learned that involve the frequency of oscillation? What about the work (or energy) of a dipole in a uniform magnetic field?
 

Related to Rotational Inertia of compass needle

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is dependent on the mass and distribution of the object's mass around its axis of rotation.

2. How does rotational inertia affect a compass needle?

The rotational inertia of a compass needle is what allows it to align itself with Earth's magnetic field and maintain its direction. The needle's mass and distribution determine its rotational inertia, which in turn affects its sensitivity to magnetic fields.

3. Can the rotational inertia of a compass needle be changed?

Yes, the rotational inertia of a compass needle can be changed by altering its mass or distribution of mass. For example, adding weight to one side of the needle will increase its rotational inertia and make it less sensitive to changes in magnetic fields.

4. How does the shape of a compass needle affect its rotational inertia?

The shape of a compass needle can affect its rotational inertia by changing its distribution of mass. A longer and thinner needle will have a higher rotational inertia than a shorter and thicker needle, as more of its mass is distributed farther from its axis of rotation.

5. What factors influence the rotational inertia of a compass needle?

The rotational inertia of a compass needle is primarily influenced by its mass and distribution of mass, but other factors such as its shape, size, and material can also play a role. Additionally, external factors like friction and air resistance can affect the needle's rotational inertia.

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