Twin skaters approach one another as shown in the figure below and lock hands. (a) (b) (a) Calculate their final angular velocity in rad/s, given each had an initial speed of 1.80 m/s relative to the ice. Each has a mass of 70 kg, and their centers of mass are 0.890 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. X What is the angular momentum of an object moving with a linear velocity about a given point? rad/s (b) Compare the initial and final kinetic energy. KE₁ KEf Initially the two skaters have translational motion while after the collision it is purely rotational. X

A disk of M = 5kg, radius R = 3m is rotating %3D %3D counterclockwise about its center with an angular speed of wi = 3rad/s. 1m and mass 2 kg is %3D a) A thin hoop of radius R dropped on the disk so that it lands on the disk's surface and they share a center the angular speed of the pair %D after the collision? b) find the angular speed of the system if the hoop lands by the edge of the disk, so that the edge of the hoop is 0.5 m away from the center of the disk Overhead view a) b) 0.5m

A yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle. a) Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius.  b)  Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.46 m.

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A wagon wheel heading down south from the land of the pines consists of a thin ring having a mass of me and six spokes made from slender rods with each having a mass of m,.. Tw Variable Value mc 7 kg mr 1.3 kg Tw 0.85 m a.) What is the moment of inertia through the center of the wheel in kg - m²? b.) What is the moment of inertia about point A in kg - m²?? A

Calculate the moment of inertia of a disc which has mass 2982.4g and radius of 0.386m. Express you result in SI units and with two decimals. Answer:

Four (4) masses 150 grams each are connected by 4 cords forming a rectangle. Thelength of the cords are 60 cm and 40 cm. determine the moment of inertial of the massesabout the axis of rotation AB (a) if AB is located at the center of longer cords, (b) AB islocated at the center of shorter cords. Ignore the mass of rod.

A 200kg disk with a radius of 4.0m is rotating clockwise about the +y axis. A 50kg person is sitting 2.5m from the rotational axis. a) What is the total moment of inertia of the disk and person together? b) What is the initial angular momentum Li of the system? c) A constant 30.0N force is applied to the edge of the disk with an angle of 60° with respect to the moment arm. (+y out of page in top down view) What is the torque on the system? d) What is the final angular momentum if the torque is applied for 2s?

A reasonable estimate of the moment of inertia of an ice skater spinning with her arms at her sides can be made by modeling most of her body as a uniform cylinder. Suppose the skater has a mass of 64 kg . One eighth of that mass is in her arms, which are 60 cm long and 20 cm from the vertical axis about which she rotates. The rest of her mass is approximately in the form of a 20 cm -radius cylinder.Estimate the skater's moment of inertia to two significant figures.

Two astronauts, each having a mass of 75.5 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 4.90 m/s. Treating the astronauts as particles, calculate each of the following. Center of gravity (a) the magnitude of the angular momentum of the system kg-m²/s (b) the rotational energy of the system KJ By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? kg-m²/s (d) What are their new speeds? m/s (e) What is the new rotational energy of the system? KJ (f) How much work is done by the astronauts in shortening the rope? kJ