The concept of centre of mass has been rightly described by admin. Consider a ball thrown vertically up in the air with a spin provided to it. A point on the surface of the ball will follow a complicated path in space owing to the spin. But the centre of the ball will follow a sraight vertical path. Hence, it is easier to describe the motion of the ball in terms of its centre of mass than in terms of point particles distributed over the entire mass of the ball.
Moment of Inertia: Linear acceleration of a body is proportional to force applied to it and described as: F = ma, where m is the mass of the body. Similarly, when we talk about a body in rotational motion about an axis, its angular acceleration is proportional to the total torque on the body.
Consider a body rotating about a fixed axis: Then, radial acceleration of a particle at distance r from the axis is v2/r = 2 r
Radial force = m2r. ----- (1)
Tangential acceleration = dv/dt Tangenial force = m dv/dt = mr d/dt = mr. ------ (2)
Torque due to (1) about the axis is zero as it intersects the axis. Torque due to (2) is mr2.
Summing over all particles, Total torque = [i]miri2 = I,
where I = [i]miri2 is the moment of inertia of the body about the axis of rotation. Moment of inertia depends upon the choice of the axis of rotation.
Hope that clears your concept of moment of inertia.
Moderation Team
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2 r
. ------ (2)
miri2
