"A playground merry-go-round of radius R = 2.00 m has a moment of inertia I= 250 kg m and is rotating at 10 rev/min about a frictionless, vertical axle. Facing the axle, a 25 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? (7.14 rev/min)

A turntable (disk) of radius r = 27.0 cm and rotational inertia 0.440 kg · m2 rotates with an angular speed of 2.98 rad/s around a frictionless, vertical axle. A wad of clay of mass m = 0.242 kg drops onto and sticks to the edge of the turntable. What is the new angular speed of the turntable? (A) _______ rad/s

A way to test the tensile strength of a wire is to place a mass at the end of it and spin the mass with uniform circular motion. The speed at which the wire breaks is a measure of its strength. The maximum frequency of rotation before a certain wire breaks is 35.5 Hz. The wire is 50.5 cm long and has a mass of 0.656 kg. (a) Determine the speed with which the mass moves. (b) Calculate the centripetal force acting on the wire

A girl of mass 31.8 kg stands on the rim of a frictionless merry-go-round of radius 1.63 m and rotational inertia 313 kg-m2 that is not moving. She throws a rock of mass 948 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 3.26 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl? (a) Number i Units (b) Number i Units

A playground merry-go-round of radius R = 1.20 m has a moment of inertia / = 255 kg-m2 and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 24.0-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? {convert units} O 0.647 rad/s O 1.11 rad/s O 0.375 rad/s O 1.31 rad/s O 0.980 rad/s MacBook Air

In the figure here, a cylinder having a mass of 1.5 kg can rotate about its central axis through point O. Forces are applied as shown: F₁ = 3.1 N, F2 = 9.3 N, F3 = 6.0 N, and F4 = 9.1 N. Also, r = 7.0 cm and R = 17 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number FA Rotation axis F₁ Unit 7

In the figure here, a cylinder having a mass of 2.8 kg can rotate about its central axis through point O. Forces are applied as shown: F1= 9.7 N, F2 = 8.3 N, F3 = 1.8 N, and F4 = 4.5 N. Also, r = 4.3 cm and R = 10 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) %3D Rotation axis Number Unit

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

A string holds and wraps around a solid cylinder (7-kg and R = 3-m). A person pulls the string vertically upward, so the cylinder’s center of gravity does not move and is suspended in midair for 3 second. Note that the rotational inertia of the cylinder about its axis is MR2/2, the tension in the string is 3-N. what is the net force on the cylinder in Newton?

In the figure here, a cylinder having a mass of 4.3 kg can rotate about its central axis through point O. Forces are applied as shown: F1 = 4.7 N, F2 = 3.6 N, F3 = 6.1 N, and F4 = 2.3 N. Also, r = 5.3 cm and R = 15 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)