Hey im so confused about moment of inertia. ?

In summary, the moment of inertia is a measure of how mass is distributed throughout an object and how it affects angular momentum and energy. It is calculated by multiplying the mass of each part of the object by its distance squared from the axis of rotation. This explains why, in the seesaw example, the farther the object is from the axis of rotation, the less torque is needed to cause rotation. This is because the moment of inertia increases with distance, making it easier to rotate the object. Torque is not something that is "needed to cause rotation" but rather a measure of the rate of change of angular momentum. The MI formula is similar to the standard deviation formula in statistics.
  • #1
reyrey389
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I=mr^2 I know moment of inertia depends on how for a object how far a bit of mass of that object is from the axis of rotation. i.e. farther from the axis = higher moment of inertia-= more torque is needed to cause rotation. this just doesn't make any sense for the seesaw example, on the seesaw the farther the object is from the axis of rotation, the LESS torque you actually need. (you need more torque closer to the pivot) this e.g. just contradicts my first sentence.

can you please help I've been confused on this for quite awhile...
 
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  • #2
Torque is not something that is "needed to cause rotation". Torque is the rate of change of angular momentum and a good way to think about is, is like you do about forces. The second law is F=ma similarly T=lα where α is the angular acceleration. When you apply a force F, on two different masses , the acceleration of the smaller mass will be higher. In the same way if you have two object of different moments of inertia and you apply the same torque the angular acceleration of the smaller l will be higher.So in the case of the seesaw if you want to have the same angular acceleration for a mass close to the pivot and one far. You will need a higher torque for the far mass and a smaller torque for the close one.
 
  • #3
Moment of inertia is telling you how your mass is distributed throughout your object (it literally is a moment), and, therefore, how angular momentum and energy act on it.
 
  • #4
A good way to think about this (given by Richard Feynman) is to think about a door, partly open. With one finger try to close it by pressing hard near the hinge edge - almost impossible. Now apply the same force near the edge away from the henge - easy.
 
  • #5
reyrey389 said:
for the seesaw example, on the seesaw the farther the object is from the axis of rotation, the LESS torque you actually need.
The farther your friend is from the pivot point, the MORE torque you need to balance his weight. :shy:
 
  • #6
sambristol said:
A good way to think about this (given by Richard Feynman) is to think about a door, partly open. With one finger try to close it by pressing hard near the hinge edge - almost impossible. Now apply the same force near the edge away from the henge - easy.

Umm. Isn't that more a matter of Moments rather than Moment of Inertia? You are accelerating the same door in each case, about the same hinge. Pushing further out just produces a given torque with less force. The MI tells you how much acceleration you will produce - it's not about the equilibrium situation.

I should say that an example to introduce the idea of MI would be to think of a mass on a light pole. The pole is on a bearing at one end and the position of the mass on the pole is adjustable. If you were to push at a point near the pivot, you would find that the angular acceleration of the mass-on-pole would be much greater when the mass is near the pivot than it would be at the end - for a given force. The angular acceleration for a given force (at a given position) is inversely proportional to the square of the distance of the mass from the pivot. The MI is Mx2, where x is the distance from the pivot.
For a set of masses (or a large object with distributed mass) you just add up all the masses times their x2s to give the total Moment of inertia.

The MI formula happens to be just the same as the Standard deviation of a statistical distribution - which used sometimes to be referred to as the second moment of a distribution.
 

1. What is the definition of moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, but instead measures an object's distribution of mass around an axis of rotation.

2. How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of each particle in an object by the square of its distance from the axis of rotation, and then summing all of these values together. It is typically represented by the symbol "I" and has units of kg*m^2.

3. What factors affect the moment of inertia of an object?

The moment of inertia of an object is affected by its mass, shape, and distribution of mass around the axis of rotation. Objects with more mass and/or mass located farther from the axis of rotation will have a higher moment of inertia.

4. How does moment of inertia relate to rotational motion?

Moment of inertia is an important factor in rotational motion because it determines how much torque is required to cause an object to rotate. Objects with a higher moment of inertia will require more torque to achieve the same rotational acceleration as objects with a lower moment of inertia.

5. Can moment of inertia be changed?

Yes, moment of inertia can be changed by altering an object's mass, shape, or distribution of mass. For example, a figure skater can change their moment of inertia by bringing their arms and legs closer to their body, decreasing their moment of inertia and allowing them to spin faster.

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