Question:
A uniform thin rod of length 1m and mass 3kg is attached to a
uniform thin circular disc of radius 30cm and mass 1kg
at its plane find the center of mass of the combination from the center of disc
Answer:
The rod is attached to the disc on its plane. Hence, the centre of disc will be the center of mass if the rod is attached uniformly on the disc.
We can also check the diagram above for clear understanding.
The moment of inertia of the combination is the moment of inertia of the rod plus the moment of inertia of the disc which is as shown in the diagram.
Hence, I = M1L2 /12 + M2R2 /2
= (3)(1)2/12 + 1(30* 10-2)2 /2
= 4 + (4.5 * 10-2) Kg m2
= 4.045 Kg m2
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