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jenyasd209 [6]
3 years ago
10

The kinetic energy of a rotating body is generally written as K=12Iω2, where I is the moment of inertia (also known as rotationa

l inertia) of the body. Find the moment of inertia of the particle described in the problem introduction with respect to the axis about which it is rotating. Assume ω = 34.0 rad/s .
Physics
1 answer:
agasfer [191]3 years ago
4 0

Answer

given,

expression of Kinetic energy of rotating body

K = \dfrac{1}{2}I\omega^2

ω = 34.0 rad/s

Assuming mass of the particle equal to 13 Kg

and perpendicular distance from the particle to the axis is r = 1.25 m

now,

moment of inertia of particle = ?

from the given expression

I= \dfrac{2K}{\omega^2}..............(1)

we know

K = \dfrac{1}{2}mv^2

v = r ω

K = \dfrac{1}{2}mr^2\omega^2

putting value in equation (1)

I= \dfrac{2\dfrac{1}{2}mr^2\omega^2}{\omega^2}

I =mr^2

I =13 \times 1.25^2

I = 20.3125 kg.m²

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