1. Kinetic energy of a rotating body : (1) Consider a rigid body rotating with a constant angular velocity w about an axis passing through the point O and perpendicular to the plane of the figure. Suppose that the body is made up of N particles of masses m1,m2,m3 situated at perpendicular distancesr1,r2,.....,rN, respectively, from the axis of rotation as shown in Fig. 1.30.
As the body rotates, all the particles perform uniform circular motion with the same angular velocity of. However, they have different linear speeds depending upon their distances from the axis of rotation.
The linear speed of the particle with mass m1 is v1= r1w. Therefore, its kinetic energy is
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