Question

A uniform cylindrical turntable of radius 1.80 m and mass 25.0 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4T rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass 2.28 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.70 m to the east of the axis. (a) Find the final angular speed of the clay and turntable. magnitude rad/s Select direction (b) Is mechanical energy of the turntable-clay system constant in this process? Yes ONo What, if any, is thé change in internal energy? (c) Is momentum of the system constant in this process? O Yes O No What, if any, is the amount of impulse imparted by the bearing? kg m/s magnitude -Select- direction

Answer 1

a. The lump of clay of negligible Seze will only change the moment of Certia by ă Shift of more the angular momentum will be Conserved in this belastic process. L = Iw = I'w Metoo - Tmagat mon) wo? MR²% MR2 W'= -1 1 + axa.asy 1.70 85 1.802 Counter Clockwise w = 10.8079 rad/sec Its direction is b. Inelastic Colloding and sticking of lump Of Clay will not allow mechanical Energy Convergeon and there will be logs s internal Energy. Thos loss Cas be. Calculated by taking the difference an Kinetic Energy, Ismo? = 25x1.802 = 405 kg.co2 & Il=It my? = 40.5+2.88x1.702 = 47.0892 kqoros?

Ake = 1/2 I'w'? Iw² = 5 [47.0892x10.802-40.5x(40)2) o the linear moentum of the the bearing is just 1. = -451.509682 J The linear momentum of the system is not Cosseoved and the compulse imparted by the beasing is just the change in linear momentum which Corresponds to the momentum omentum gaised gained by the Cump of clay as it stecks to the rotating turntable Impulse = mv = moco = 2.28x1.70 x 10.80 = 41.8609 kq in