Question

A GRINDING WHEEL OF MASS 5 KG AND DIAMETER 0.4M IS ROTATING WHITH AN ANGULAR SPEED OF 2 REV S CALCULATE THE TORQUE WHICH WILL INCREASE ITS ANGULAR SPEED TO 8 REVOLUTION PER SECOND IN 2s.

Answer 1

given : mass M= 5 kg

          diameter D = 0.4 m

         radius R = D÷2=  0.4÷2=    0.2 m

         n1 = 2 rps

         n2 = 8 rps

        T = 2 sec

torque = I×α...............eq (1)

momeny of inertia of wheel is I = MR²

                                                    = 5 ×(0.2)²

                                                   = 5 × 0.4

                                                  I = 2................(2)

angular acceleration α=(ω2-ω1)÷T

                                =    ( 2πn2 - 2πn1 )÷2

                                = 2π(8-2)÷2

                               = 6π

                                = 18.84 ........(3)

            put the values of  equation 2 and 3 in eq 1 we get

 torque =  2×18.84

            = 37.68 Nm