A uniform disk (1=1/2 mR2) has a mass of 3 kg and a radius of 2m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 120 rpm (revolutions per minute, convert it to rad/s). A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. (HINT: Note that some of the information given is not needed! Think which conservation law(s) apply.) The final angular momentum of the system is closest to: L= |Π| ΑΣΦ Submit Request Answer ? kg. m²/s 4

A small object with mass 4.45 kg moves counterclockwise with constant speed 1.60 rad/s in a circle of radius 2.75 m centered at the origin. It starts at the point with position vector 2.75î m. Then it undergoes an angular displacement of 9.10 rad. (a) What is its new position vector? m (b) In what guadrant is the object located and what angle does its position vector make with the positive x-axis? --Select--- v at (c) What is its velocity? m/s (d) In what direction is it moving? o from the +x direction. (e) What is its acceleration? m/s2 (f) Make a sketch of its position, velocity, and acceleration vectors. Choose File No file chosen (g) What total force is exerted on the object? N

A hollow spherical shell has mass 8.50 kg and radius 0.240 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.875 rad/s2. What is the kinetic energy of the shell after it has turned through 6.50 rev?

A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.110 m, an angular speed of 50.0 rad/s, and a moment of inertia of 1.26 kg·m2. A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 3 during a time of 8.00 s.  Find the magnitude of the angular deceleration of the cylinder.

A solid horizontal cylinder rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. The mass of cylinder is mass 10.8 kg and its radius 1.00 m.   If a piece of putty (m= 0.250-kg ) is dropped vertically onto the cylinder and sticks at a point 0.900 m from the center of rotation, what will be the final angular speed of the system.

The figure shows a uniform disk that can rotate around its center like a merry-go-round. The disk has a radius of 1.8 cm and a mass of 22 grams and is initially at rest. Starting at time t = 0, two forces are to be applied tangentially to the rim as indicated, so that at time t = 1.3s the disk has an angular velocity of 210 rad/s counterclockwise. Force F₁ has a magnitude of 0.105 N. What is magnitude F₂? F Number Units F2

The left-hand end of a uniform rod of length L and mass m is attached to a vertical wall by a frictionless hinge. The rod is held at an angle θ above the horizontal by a horizontal wire that runs between the wall and the right-hand end of the rod. The wire breaks and the rod rotates about the hinge. What is the angular speed of the rod as the rod passes through a horizontal position? (Express your answer in terms of some or all of the variables m, g, L, θ.)

A Texas cockroach of mass 0.246 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 18.0 cm, rotational inertia 3.36 x 10³ kg-m?, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.75 m/s, and the lazy Susan turns clockwise with angular velocity wo = 3.31 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? (a) Number Units (b)

A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 55.0 kg that rests on a platform. The cylinder has a mass of 255 kg and a radius of 0.490 m. Assume that the cylinder can rotate about its axis without any friction and the rope is of negligible mass. The platform is suddenly removed from under the block. The block falls down toward the ground and as it does so, it causes the rope to unwind and the cylinder to rotate. (a) What is the angular acceleration, in rad/s², of the cylinder? rad/s2 (b) How many revolutions does the cylinder make in 5 s? rev (c) How much of the rope, in meters, unwinds in this time interval?

A pulley attached to the top of a ramp has a rope wrapped around it (like a spoon of thread). Treat the pulley like a solid cylinder. The rope is attached to a solid sphere at its axle. The axle turns without friction. The system is released from rest. The rope unwinds from the pulley and the sphere rolls without slipping down the hill. The mass of the pulley is 20.0kg and has a radius of 0.250m. The 8. sphere has a mass of 50.0kg and a radius of 0.500m. The ramp makes an angle of 40.0° with the horizontal. (Solve this problem using Force-Torque Principles.) What is the acceleration of the sphere? а. b. What are the angular accelerations of the pulley and the sphere?