What is the axis for #21 on Moment of Inertia?

In summary, the conversation involves someone seeking help with problem #21, specifically regarding the axis and how to use the parallel axis theorem to calculate inertia. They have already found the inertia with respect to the center in problem #20 and are now trying to determine the values of D and M. The expert provides the formula for the parallel axis theorem and explains that Icm is the inertia with respect to the center, D is the distance from the center of mass to the point of rotation (in this case, equal to the radius of the hoop), and M is the total mass. They also confirm that Icm is the answer for #20.
  • #1
muna580
http://img100.imageshack.us/img100/1756/untitled2qx1.jpg [Broken]

I am having trouble with #21. I already did #20, but I have NO idea of how to do #21. First of all, I am not really sure where is the axis suppose to be.
 
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  • #2
muna580 said:
I am having trouble with #21. I already did #20, but I have NO idea of how to do #21. First of all, I am not really sure where is the axis suppose to be.

Use the parallel axis theorem. Put the axis through the tip of the arrow in the diagram
 
  • #3
Acorrding to the parallel axis theorm, you get the inertia by dong this

I = Icm + D^2M

Where Icm is the inertia with respect to the center, and D is the distnance, and M is the mass.

Well, Icm is the answer I got for #20 right?

Also, what do I use for the D? Is D the radius?

Also, what is M? Is M the mass for the hoop plus the mass of all the 4 spokes?
 
  • #4
muna580 said:
Acorrding to the parallel axis theorm, you get the inertia by dong this

I = Icm + D^2M

Where Icm is the inertia with respect to the center, and D is the distnance, and M is the mass.

Well, Icm is the answer I got for #20 right?

Also, what do I use for the D? Is D the radius?

Also, what is M? Is M the mass for the hoop plus the mass of all the 4 spokes?

Yes. Icm is what you found in #20.

M is the total mass and D is the distance from the center of mass to the point of rotation. In this case, D = radius
 

What is the axis for #21 on Moment of Inertia?

The axis for #21 on Moment of Inertia is the line or axis around which an object's mass is evenly distributed. It is used to calculate an object's resistance to rotational motion.

Why is the axis for #21 on Moment of Inertia important?

The axis for #21 on Moment of Inertia is important because it helps determine how an object will behave when subjected to forces that cause it to rotate. It is essential in understanding an object's stability and how it will respond to external forces.

How is the axis for #21 on Moment of Inertia calculated?

The axis for #21 on Moment of Inertia is calculated by summing the products of each particle's mass and the square of its distance from the axis of rotation. This calculation can be done using integrals or by using the parallel axis theorem.

Can the axis for #21 on Moment of Inertia change?

Yes, the axis for #21 on Moment of Inertia can change depending on the object's shape, orientation, and the axis of rotation. It can also change if there is a redistribution of mass within the object.

How does the axis for #21 on Moment of Inertia affect an object's rotational motion?

The axis for #21 on Moment of Inertia affects an object's rotational motion by determining its rotational speed and acceleration. Objects with a larger moment of inertia will have a slower rotational speed and require more torque to accelerate, while objects with a smaller moment of inertia will have a faster rotational speed and require less torque to accelerate.

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