A 3.0-kg cart is rolling along a frictionless, horizontal track towards a 1.9-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is +5.7 m/s, and the second cart's velocity is -1.7 m/s. (a) What is the total momentum of the system of the two carts at this instant? (b) What was the velocity of the first cart when the second cart was still at rest? (a) Number i Units (b) Number i Units CA two-stage rocket moves in space at a constant velocity of +4810 m/s. The two stages are then separated by a small explosive charge placed between them. Immediately after the explosion the velocity of the 1190-kg upper stage is +5770 m/s. What is the velocity (magnitude and direction) of the 2770-kg lower stage immediately after the explosion? Number i UnitsThe earth spins on its axis once a day and orbits the sun once a year (365 1/4 days). Determine the average angular velocity (in rad/s) of the earth as it (a) spins on its axis and (b) orbits the sun. In each case, take the positive direction for the angular displacement to be the direction of the earth's motion. (a) Number Units C (b) Number Units CA floor polisher has a rotating disk that has a 16-cm radius. The disk rotates at a constant angular velocity of 1.6 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 54 s, in order to buff an especially scuffed area of the floor. How far does a spot on the outer edge of the disk move during this time? Number i Units CA clay vase on a potter's wheel experiences an angular acceleration of 8.68 rad/s due to the application of a 12.7-N m net torque. Find the total moment of inertia of the vase and potter's wheel. Number i Units CTwo thin rods of length L are rotating with the same angular speed w (in rad/s) about axes that pass perpendicularly through one end. Rod A is massless but has a particle of mass 0.64 kg attached to its free end. Rod B has a mass of 0.64 kg, which is distributed uniformly along its length. The length of each rod is 0.78 m, and the angular speed is 4.2 rad/s. Find the kinetic energies of rod A with its attached particle and of rod B. (a) KEA = (b) KEB = iA playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.67 m, an initial angular speed of 3.49 rad/s, and a moment of inertia of 122 kg.m2. The mass of the person is 49.6 kg. Find the final angular speed of the carousel after the person climbs aboard. Wf = i C