Question

Derive an expression for kinetic energy of a body rotating about an axic with uniform angular velocity

Answer 1

we know, translation kinetic energy , K.E=\frac{1}{2}mv^2,

when a body of mass ‘ m ’ moves with uniform angular velocity, \omega and position of body from the axis of rotation r .

then, linear velocity of body v=\omega r

so, rotational kinetic energy of body is given by

K.E=\frac{1}{2}m(\omega r)^2

or, K.E=\frac{1}{2}m\omega^2r^2

or, K.E=\frac{1}{2}(mr^2)\omega^2

we know, moment of inertia is the product of mass and square of separation between position of particle and axis of rotation.

e.g.,. I=mr^2

so, K.E=\frac{1}{2}I\omega^2 it is the expression for kinetic energy of a rotating body with uniform angular velocity

Answer 2

Answer:

hyy mate

above answer is right