A cylinder of mass 12.0 kg rolls without slipping on a horizontal surface. At the instant its center of mass has a speed of 12.0 m/s, determine the following energies. ROTATIONAL KE, and toltal energy. #2: The position vector of a particle of mass 3.50 kg is given as a function of time by r = (7.00 i + 8.00t j ) m. Determine the angular momentum of the particle as a function of time. #3: A student sits on a rotating stool holding two weights, each of mass 3.00 kg. When his arms are extended horizontally, the weights are 0.900 m from the axis of rotation and he rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg · m2 and is assumed to be constant. The student pulls the weights horizontally to 0.300 m from the rotation axis. Find angular velicty of student, Find KE of student before weights pulled in, and Find KE of student after weights pulled in. #4 A space station shaped like a giant wheel has a radius of 100 m and a moment of inertia of 6.00 108 kg · m2. A crew of 150 are living on the rim, and the station's rotation causes the crew to experience an acceleration of 1g (Fig. P10.47). When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 75.0 kg.