Question

A grinding wheel of mass 0.5 kg & diameter 0.4m is rotating with an angular speed of 2 rev s^-1. Calculate the torque which will increase it's angular speed to 8 revolution per second in 2sec.

Answer 1

118pawarchaitaliu Ambitious

given : mass M= 0.5 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

                                                    = 0.5 ×(0.2)²

                                                   = 0.5 × 0.04

                                                  I = 0.02.........(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 =  0.02×18.84

            = 0.3768 Nm