Question

State and prove theorem of parallel axes.

Answer 1

Answer:

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.

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Answer 2

$\large{\star{\underline{\textsf{Theorem of Parallel axes:-}}}}$

• Moment of Inertia (MI) of a body about any axis is equal to sum of its moments of Inertia of a body about a parallel axis passing through its centre of mass and product of its mass and square of distance between axes.

$\large{\star{\underline{\textsf{Proof:-}}}}$

→ I = sigma m (x+d)²

→ sigma m (x²+d²+2xd)

→ sigms m x²+ sigma md² +2 sigma mxd

→ Icm+md²+2×0

→I = Icm+md²