In the figure, two skaters, each of mass 49.2 kg, approach each other along parallel paths separated by 2.60 m. They have oppositevelocities of 1.52 m/s each. One skater carries one end of a long pole of negligible mass, and the other skater grabs the other end asshe passes. The skaters then rotate about the center of the pole. Assume that the friction between skates and ice is negligible. Whatare (a) the radius of the circle, (b) the angular speed of the skaters, and (c) the kinetic energy of the two-skater system? Next, theskaters each pull along the pole until they are separated by 1.87 m. What then are (d) their angular speed and (e) the kineticenergy of the system?(a) NumberUnits(b) NumberUnits(c) NumberUnits(d) NumberUnits(e) NumberUnits

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 51P

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A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.
A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through one of its ends. Find the magnitude of the rodsangular momentum.
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Two astronauts (Fig. P10.67), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.
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A uniform disk of mass m = 10.0 kg and radius r = 34.0 cm mounted on a frictionlessaxle through its center, and initially at rest, isacted upon by two tangential forces of equalmagnitude F, acting on opposite sides of itsrim until a point on the rim experiences acentripetal acceleration of 4.00 m/s2 (Fig.P13.73). a. What is the angular momentumof the disk at this time? b. If F = 2.00 N, howlong do the forces have to be applied to thedisk to achieve this centripetal acceleration? FIGURE P13.73
The position vector of a particle of mass 2.00 kg as a function of time is given by r=(6.00i+5.00tj), where r is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time.
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A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-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?
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