how moment of inertia is equals to 1/2 MR2 ?
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The moment of inertia(I) of a body about an axis is given by
I = m r2
Where m = mass of a body
r = perpendicular distance of mass m from the axis of of rotation
For cases when the body is revolving around an axis passing through its own centre like for uniform circular ring is revolving about a diameter or uniform circular disc is rotating about an axis passing through centre and perpendicular to its plane.
I = (1/2) mr2
HOPE THIS HELPS...
I = m r2
Where m = mass of a body
r = perpendicular distance of mass m from the axis of of rotation
For cases when the body is revolving around an axis passing through its own centre like for uniform circular ring is revolving about a diameter or uniform circular disc is rotating about an axis passing through centre and perpendicular to its plane.
I = (1/2) mr2
HOPE THIS HELPS...
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0
The moment of inertia (I), however, is always specified with respect to that axis and is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis.
Explanation:
Since force can be expressed as mass times acceleration (mass·length/time2), these units for moment of inertia can be seen to be equivalent to units of (mass·length2). Computing torque in the English system with the equation T=J·α is straightforward, as well.
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