Question
State and prove the theorem of parallel axis.
Solution
Statement:
The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to axis passing through centre of mass is equal to the sum of the moment of inertia of body about an axis passing through centre of mass and product of mass and square of distance between the two axes.
The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to axis passing through centre of mass is equal to the sum of the moment of inertia of body about an axis passing through centre of mass and product of mass and square of distance between the two axes.
Proof:
Let, IC be the moment of inertia of about an axis passing through the centre of mass i.e. about AB and I be the moment of inertia about axis A' B' at a distance h.
Let, IC be the moment of inertia of about an axis passing through the centre of mass i.e. about AB and I be the moment of inertia about axis A' B' at a distance h.
Then,
I =Ic + Mh2
Consider, a particle of mass m at a distance r from the centre of gravity of the body.
Hene the result.
