Short webpage title: Calculating Moments of Inertia and Magnetic Moment

[besnik93]

Homework Statement

For any flat object, located in the x-y plan applies to the equation:
I_x+I_y=I_z

where I_x,I_y,I_z is the moments of inertia about the x-axis, y-axis and z-axis.
A flat circular coil has n windings and radius r. The mass of the coil is m. The coil is located in the x-y plan centered on (0,0). The coil moment of inertia about the z-axis is called I_z

a) Give a formula of I_z. Also specify a formula for I_x and I_y.

The coil has one turn. The current in the coil is I.
b) Give the magnetic moment μ of the coil.

The Attempt at a Solution

a+b) I am thinking of using the definition of the magnetic moment of a current loop, but i can't get further, can someone help please?

 

[paisiello2]

Kind of a strange question since it asks two completely different questions:

a) Do you know formula for the mass moment of inertia for a ring?

b) Yes, simply use the definition for a magnetic moment of a coil.

 

[besnik93]

[
a) Do you know formula for the mass moment of inertia for a ring?

Is it K= rootof(Ic/m)?

 

[paisiello2]

No, it's Iz we're after.

 

[HalfLostAndSearching]

a) The moment of inertia of a flat object about a particular axis is given by the formula I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation. In this case, for the coil located in the x-y plane, the moments of inertia about the x-axis and y-axis would be given by:

Ix = mr^2
Iy = mr^2

Since the coil is located in the x-y plane, the moment of inertia about the z-axis (perpendicular to the plane) would be given by:

Iz = m(r^2 + r^2) = 2mr^2

b) The magnetic moment of a current loop is given by the formula μ = IA, where I is the current in the loop and A is the area enclosed by the loop. In this case, since the coil has one turn, the area enclosed by the loop would be πr^2. Therefore, the magnetic moment of the coil would be:

μ = IA = (I)(πr^2) = Iπr^2