Parallel and perpendicuar axis theorems and other stuff on rotational mechanics

[**spark**]

Hi,
I've been doing rotational mechanics at school and at the end of the chapter,the parallel and perpendicular axis theorems appear to have sprung out of nowhere!

The proofs are given in the book but somehow, they don't make any sense.

I can't understand their implications in the real physical world,their origin,their logical meaning.

I mean,there must be something more to these theorems rather than only their mathematical proofs!

Please would someone guide me?

 

[**spark**]

No help?? :(

 

[Lok]

It would help if we knew what theorems you are talking about like maybe momentum etc.
What theorems exactly? Give a solution and the problem can be found :P.

 

[annatar]

I guess the OP is talking about the theorems that help us to find centers of masses

 

[**spark**]

Sorry,I meant the theorems that help us find the moment of inertia.

The theorem of parallel axes says that the moment of inertia of an object about any axis parallel to an axis through the centre of the object and at a distance d from it is I+M(d squared),where I is the moment of inertia about the axis through the centre and M is the mass of the object.

The theorem of perpendicular axis says that the moment of inertia about an axis is equal to the sum of moments of inertia about any 2 axes mutually perpendicular and meeting at the third axis(aboout which we are calculating the moment of inertia)

 

[Doc Al]

Did you have a specific question about these theorems?

Note that the perpendicular axis theorem applies to planar (flat) bodies.

 

[Bob S]

The parallel axis theorem is actually quite simple. If a body of mass M has a moment of inertia I₀ about an axis through its center of mass, then its moment of inertia about another parallel axis displaced by a perpendicular distance b, then the additional moment of inertia is Mb²: I' = I₀ + Mb². The additional term may be recognized as the moment of inertia of a point mass M at the end of a massless rod of length b. This would apply, for example, to a pendulum with a finite-size mass at the end of the rod.