Kinetic energy of a rotating body

Kinetic energy of a rotating body

We know that any moving object posses kinetic energy due to it's velocity. When a body rotates about ant axis as then this rotational kinetic energy  comes into the picture. Let us study this topic in details.

Figure A

Consider a rigid body made up of n no of particles as shown in fig A. Let m₁,m_2,m₃,m_n are the mass of each particle and r₁,r_2,r_3,r_n be the perpendicular distance from axis of rotation and v₁,v_2,v₃,v_n be the linear velocity respectively. The body is rotating about an axis passing through point O.

Mathematically, KE = 1/2mv²

From equation (A) and (B), it is clear that mass in translation motion is analogous to moment of inertia in rotational motion.

Equation (A) give kinetic energy of a rotating body.

│<<<Vertical circular Motion││Moment of inertia>>>│

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