Atexas cockroach of mass 0.213 kg runs counterclockwise around the rim of a lazy susan (a circular disk mounted on a vertical axle) that has a radius 17.7 cm, rotational inertia 5.12 x 10-3 kg·m2, and frictionless bearings. the cockroach's speed (relative to the ground) is 2.92 m/s, and the lazy susan turns clockwise with angular velocity ω0 = 3.05 rad/s. the cockroach finds a bread crumb on the rim and, of course, stops.
(a) what is the angular speed of the lazy susan after the cockroach stops?
(b) is mechanical energy conserved as it stops?

State the following: boyle's law and charle's law

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?