I don\'t know where to begin with this problem! A motor applies a torque of 1.41

Question

I don't know where to begin with this problem! A motor applies a torque of 1.41 Nm for 4 seconds to astationary dylindircal turntable of mass 10 kg and radius 0.3 m,causing it to rotate. The motor is then switched off and theturntable rotates at a constant angualr velocity in the abscence ofa net external torque. A non-rotating hoop of the same mass andidentical radius is then dropped onto the turntable and the twoobjects rotate in unison, Assuming that no net torques act on thesystem at this point, find the anular velocity of the hoop and diskas they rotate together. I don't know where to begin with this problem! A motor applies a torque of 1.41 Nm for 4 seconds to astationary dylindircal turntable of mass 10 kg and radius 0.3 m,causing it to rotate. The motor is then switched off and theturntable rotates at a constant angualr velocity in the abscence ofa net external torque. A non-rotating hoop of the same mass andidentical radius is then dropped onto the turntable and the twoobjects rotate in unison, Assuming that no net torques act on thesystem at this point, find the anular velocity of the hoop and diskas they rotate together.

Explanation / Answer

   Moment of inertia of table, I1 = 0.5MR2 = 0.5 x 10 x 0.09 = 0.45 kg-m2    Moment of inertia of hoop, I2 = MR2 =10 x 0.09 = 0.9 kg-m2    = / I1 = 1.41 / 0.45 = 3.1333rad/s2    = o + t = 0 + 3.13333 x4 = 12.53333 rad/s Angular momentum of table = I1 x = 5.64 Nm-s Now, as hoop is dropped on the table no external torqueacted on (table + cylinder system) Angular momentum initial and final will remainconserve Let final angular velocity = ' Final angular momentum = (I1 + I2)' = 1.35' 1.35' = 5.64    ' = 4.1777 rad/s

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