(a) Find the moment of inertia of a thin metre scale about a perpendicular axis through the centre. Take M as the mass of the scale. (b) Find the moment of inertia of a thin circular disc of mass m and radius R about one of its diameters. (c) If a student fixes two discs each of radius R at the ends of meter scale and rotates the system about an axis perpendicular to the length of the scale as in figure. What will be the moment of inertia of the system?
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Answer:
0.1458kg.msquare
Explanation:
M=1kg,L=1m
Let Icm and I be the moment of inertia of the rod about a transverse axis through it's centre ,and a parallel axis Midway between it's centre and one end.
Then,Icm =MLsquare/12 and h=L/4
by the theorem of parallel axis
I=Icm+Mhsquare
MLsquare/12+MLsquare/16=4MLsquare/48
=7/48MLsquare=7/48(1)(1)(1)=0.1458kg.msquare
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