Question

A uniform 0.030 kg rod of length 0.40 m rotates in a horizontal plane about a fixed vertical axis through its center. Two small rings, each with a mass of 0.020 kg can slide along the rod. They are initially held by catches at a position 0.050 m on either side of the rod’s center. The rod is rotationally accelerated to 30.0 rpm and then left to spin freely with no friction. While the rod is spinning, the catches are released are the rings begin to slide towards the ends of the rod.

(a) Draw and label a diagram of this problem.

(b) What is the initial acceleration of the rings along the rod just after the catches are released?

(c) What is the angular speed of the rod and rings when the rings reach the end of the rod?

(d) What is the angular speed of the rod after the rings have slipped off the ends of the rod?

Answer 1

Note : In part d there can be two cases. in one case we have to the rings coming out of the rod and still maintaining there angular velocity. In that case the answer to d part will be same as of that in c part. else if we assume that the rings are suddenly removed and does not carry out the momentum of the rod than the solution is given below.

System censite a rod amd d rings Anvrtia of Let moment System L. Y T Trod Trings ML2 +2m2 12 cedra O.02 kg M0.03ky O.4m Wi n hal ongulan velouty Tad/s 30 rpm Tuat whent catches are Temoved 0.05m hu Cantipatal accelor at on 0.49 mls

reaches Tod's end Tring Cwhan the States mementum censeVation 2 ML 2m MLt + 12 12 uhere r0 05 m TX10X T = wp 0.23 rad/s Herce final ongulan ueloa ty -0-23 7a4/ we get. hdaning angadar ML2M mementum ML2 x TI= 2 (2 5x104x W:3.925 Tad/s