Question

if m, p and L denote mass,linear momentum and angular momentum of a particle moving in circle of radius r,then its rotational K.E cen be expressed as:​

Answer 1

The Expression for Rotational Kinetic energy is:

• Kinetic energy is given by the expression

                    $K.E = M * v^{2}/2$

              where M is the mass and v is the velocity of moving body.

• linear momentum is given as

                                 $p = M * v$

• therefore by multiplying and dividing by M, the kinetic energy expression becomes

                            $K.E = p^{2} /(2 * M)$

• Angular moment is given by

                         $L = M * v * R$

                        $L = p * R\\p = L/R$

             where R is the radius with which the particle moves.

• now substituting the above equation in the K.E expression ,we get the rotational Kinetic energy expression:

         Ans:                   $K.E = L^{2} /(2*R^{2} *M)$