Moment of Inertia Help: Calculating Away from Axis

In summary, the conversation discusses how to calculate the moment of inertia for an object that is away from the axis of rotation. The speaker is trying to determine the total angular momentum and kinetic energy of two disks, one rotating around the origin and the other connected to it and rotating at a different angular velocity. They also mention using the parallel axis theorem and summing the two disks' angular momentums to find the total momentum. The response explains that angular momentum is calculated by finding the cross product of the object's center of mass and its velocity relative to a reference point, and adding it to the spin angular momentum calculated from the object's rotation about its center of mass.
  • #1
mcsnowmo
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Moment of inertia help!

I have a question about moment of inertia. How do you calculate an object that is away from the axis of rotation? I am trying to figure out how to find the total angular momentum of two disks. One disk is rotating around the origin. Disk 2 is connected to disk 1 and is a distance L away and rotating at a different angular velocity. I am trying to figure out if i need to use the parallel axis theorem for disk 2 and if i can sum the two disk's angular momentum's to get the total momentum. I also need to find the total kinetic energy. any help would me much appreciated. thanks.
 
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  • #2


Angular momentum is calculated in two parts; first you take the cross product of the center of mass of your object with it's velocity relative to your reference point, then you find the spin angular momentum of that object which is the angular momentum it gets from spinning about its center of mass and is calculated as [itex] I \omega [/itex]. Just add these two together to find the total angular momentum about some point :)
 

FAQ: Moment of Inertia Help: Calculating Away from Axis

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotation. It is calculated based on the mass distribution of an object and the distance of the mass from the axis of rotation.

2. How is moment of inertia calculated?

Moment of inertia is calculated by summing the products of each mass element and its squared distance from the axis of rotation. This can be done using either the parallel axis theorem or the perpendicular axis theorem, depending on the shape and orientation of the object.

3. Why is moment of inertia important?

Moment of inertia is important in understanding an object's rotational dynamics, such as how it will respond to external forces or how much torque is required to achieve a certain angular acceleration. It is also used in engineering and design to determine the stability and strength of structures.

4. What is the difference between moment of inertia and mass?

Moment of inertia and mass are both measures of an object's resistance to changes in motion, but they apply to different types of motion. Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of its resistance to rotational motion.

5. How does the moment of inertia change when the axis of rotation is moved?

Generally, the moment of inertia will increase when the axis of rotation is moved further away from the mass distribution of an object. This is because the mass elements are now farther from the axis and contribute more to the overall moment of inertia calculation.

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