Question
What is the moment of inertia of a disk shaped wheel that has a mass of 15kg and a diameter of 2m
Answers
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The moment of inertia of a disk shaped wheel with a mass of 15kg and a diameter of 2m is approximately 118.5 kg m2.
mass = density * pi R^2 t = 15 but R^2 = 1
so 15 = density * pi t
density = 15 / pi t
I = m integral from r = 0 to r = 1 of 2 pi r t *r^2 *density dr
= 2 pi t * density R^4/4 but R = 1
so I = density * 2 pi t/4 = (15 / pi t) *2 pi t/4 = 7.5
so 15 = density * pi t
density = 15 / pi t
I = m integral from r = 0 to r = 1 of 2 pi r t *r^2 *density dr
= 2 pi t * density R^4/4 but R = 1
so I = density * 2 pi t/4 = (15 / pi t) *2 pi t/4 = 7.5