A horizontal plywood disk with mass 7.40kg and diameter 1.12m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.07m to the disk. A 1.40-kg , battery-driven model train rests on the tracks. To demonstrate conservation of angular momentum, you switch on the train's engine. The train moves counterclockwise, soon attaining a constant speed of 0.600m/s relative to the tracks.
a. Find the magnitude and direction of the angular velocity of the disk relative to the earth.