A student sits on a freely rotating stool holding two dumbbells, each of mass 3.08 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 0.97 m from the axis of rotation and the student rotates with an angular speed of 0.741 rad/s. The moment of inertia of the student plus stool is 2,59 kg • m? and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.307 m from the rotation axis (Figure b). (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kbefore = Kafter

A playground merry-go-round of radius R = 1.20 m has a moment of inertia I = 255 kg · m2 and is rotating at 9.0 rev/min about a frictionless vertical axle. Facing the axle, a 23.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round? rev/min Need Help? Read It Watch It

A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg-m? and is assumed to be constant. The student then pulls the objects horizontally to 0.20 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student system before and after the objects are pulled in. before after

A turntable of radius R=2.00 m and mass M=32.0 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4x rad/s. The fixed turntable bearing is frictionless. The turn table is in the shape of a uniform disc with the moment of inertia of this turntable being I 0.5*MR?. (a) What is the magnitude of angular momentum of this turntable? Answer: 803.84 (b) What is the (magnitude of) the momentum of this turntable? Answer: 401.92 kgm2/s? X kgm/s? Now a lump of clay of mass m=2.48 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to a point 1.90 m from the axis (c) Find the final angular speed of the clay and turntable. Answer: 12.386 X rad/s

Someone is standing on a frictionless platform that is rotating at 2.1 revolutions per second.  In each of their outstretched arms they are holding a weight.  The moment of inertia of the system is 8kg·m^2.  When they pull the weights in their moment of inertia decreases to 3.9kg·m^2. What is the change in kinetic energy and where did the extra energy come from?

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.04 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.08 m from the axis of rotation and the student rotates with an angular speed of 0.757 rad/s. The moment of inertia of the student plus stool is 2.73 kg m² and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.308 m from the rotation axis (Figure b). @₂ Ⓡ (a) Find the new angular speed of the student. rad/s b (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kbefore = Kafter = Need Help? Read It Watch It

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…

A student sits on a rotating stoll holding two 8.0kg objects. When his arms are extended horizontally, the objects are 1.3m from the axis rotation and he rotated with an angular speed of 1.8rad/s. The moment of intertidal of the student plus stoll is 4.5kg•m^2 and is assumed to be constant.  if the student pulls in the two objects horizontally to 0.50m from the rotation axis. What is the new angular speed in rad/s of the student? (3 sig fig)

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.07 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.06 m from the axis of rotation and the student rotates with an angular speed of 0.742 rad/s. The moment of inertia of the student plus stool is 2.73 kg· m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.291 m from the rotation axis (Figure b). w; (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kpefore Kafter