Moment of Inertia: Difference Between Equations 3 and 6

In summary, the two formulas in the paint document, numbered 3 and 6, have different purposes. Formula 3 calculates the moment of force by multiplying the force with the perpendicular distance, while formula 6 calculates the moment of inertia by converting rotation rate to angular momentum. Formula 3 would be used for questions involving gravitational force and mass at a certain offset, while formula 6 would be used for questions related to rotation and angular momentum.
  • #1
Miike012
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What is the differece between the two formulas numbered 3 and 6 in the paint document?

And what types of questions would I use eq. 3 and eq. 6?
 

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  • #2
The moment is force * perpendicular distance. Summing gives ∫F(x)x.dx. When F is gravitational and the mass at offset x is y=y(x), that's ∫gyx.dx
The moment of inertia is the factor converting rotation rate, ω, to angular momentum (sometimes called moment of momentum). An element at distance x from the axis is moving at speed xω so has linear momentum xω.dm. The moment of that is x2ω.dm. So this leads to ∫yx2.dx.
(Sorry, just realized I've swapped x and y c.w. the link you posted. Can't be bothered to swap back.)
 

FAQ: Moment of Inertia: Difference Between Equations 3 and 6

What is the difference between equations 3 and 6 in calculating moment of inertia?

Equation 3, also known as the parallel axis theorem, is used to calculate the moment of inertia of an object that is rotating about an axis that is parallel to the object's center of mass. Equation 6, also known as the perpendicular axis theorem, is used to calculate the moment of inertia of an object that is rotating about an axis that is perpendicular to the object's plane of symmetry.

Which equation should I use to calculate moment of inertia?

The equation to use depends on the specific situation. If the object is rotating about an axis that is parallel to its center of mass, use equation 3. If the object is rotating about an axis that is perpendicular to its plane of symmetry, use equation 6.

Can both equations 3 and 6 be used for any object?

No, the equations are only applicable to objects with a known plane of symmetry. In addition, equation 3 can only be used for objects with a known center of mass and equation 6 can only be used for objects with a known axis of rotation.

How do equations 3 and 6 relate to each other?

Equations 3 and 6 are related through the moment of inertia tensor. Equation 3 is a special case of equation 6, where the axis of rotation is parallel to the object's center of mass.

Can moment of inertia be negative?

No, moment of inertia is a physical quantity that represents the resistance of an object to changes in its rotational motion. It is always a positive value or zero for point masses.

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