Rotational MotionHard
Question
The moment of inertia of a thin uniform rod of mass M and length L about an axis passingthrough its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
Options
A.I0 + ML2/2
B.I0 + ML2/4
C.I0 + 2ML2
D.I0 + ML2
Solution
According to the theorem of parallel axes, the moment of inertia of the thin rod of mass M and length L about an axis passing through one of the ends is
I = ICM + M d2
Where ICM is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and d is the distance between two parallel axes.
ICM = I0, d =
∴ I = I0 + M
I = ICM + M d2
Where ICM is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and d is the distance between two parallel axes.
ICM = I0, d =
∴ I = I0 + M
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