3. An ice skater spins with arms fully extended. If she pulls her arms closer to her body then (a) the kinetic energy increases (b) the moment of inertia decreases (c) the angular momentum remains constant (d) all of these Solution/Explanation: 4. Juan Tamad is pedalling a bicycle at 10 m/s. Suppose the diameter of the bicycle wheels is 132 cm. What is the angular speed of the wheels? (a) 7.5 rad/s b) 13 rad/s c) 10 rad/s d) 15 rad/s Solution/Explanation:

3. An ice skater spins with arms fully extended. If she pulls her arms closer to her body then (a) the kinetic energy increases (b) the moment of inertia decreases (c) the angular momentum remains constant (d) all of these Solution/Explanation: 4. Juan Tamad is pedalling a bicycle at 10 m/s. Suppose the diameter of the bicycle wheels is 132 cm. What is the angular speed of the wheels? (a) 7.5 rad/s b) 13 rad/s c) 10 rad/s d) 15 rad/s Solution/Explanation:

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 6CQ: Why is the moment of inertia of a hoop that has a mass M and a radius R greater than the moment of...

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Big Ben (Fig. P10.17), the Parliament tower clock in London, has hour and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg and 100 kg, respectively. Calculate the total angular momentum of these hands about the center point. (You may model the hands as long, thin rods rotating about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)
A student rides his bicycle at a constant speed of 3.00 m/s along a straight, level road. If the bikes tires each have a radius of 0.350 m, (a) what is the tires angular speed? (See Section 7.3.) (b) What is the net torque on each tire? (See Section 8.5.)
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?
A disk of mass m is spinning freely at 6.00 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. (a) What is the angular speed of the new system? (b) If a third such disk is dropped on the first two, find the final angular speed of the system.
Why is the moment of inertia of a hoop that has a mass M and a radius R greater than the moment of inertia of a disk that has the same mass and radius? Why is the moment of inertia of a spherical shell that has a mass M and a radius R greater than that of a solid sphere that has the same mass and radius?
Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.18). The system rotates about the x axis with an angular speed of 2.00 rad/s. Find (a) the moment of inertia about the x axis, (b) the total rotational kinetic energy evaluated from 12I2, (c) the tangential speed of each particle, and (d) the total kinetic energy evaluated from 12mivi2. (e) Compare the answers for kinetic energy in parts (b) and (d). Figure P10.18
Two astronauts (Fig. P10.67), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.00 m/s. 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 astronaut shortens the distance between them to 5.00 m. (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.
A basketball player entertains the crowd by spinning a basketball on his nose. The basketball has a mass of 0.600 kg and a radius of 0.121 m. If the basketball is spinning at a rate of 3.00 revolutions per second, (a) what is its rotational kinetic energy? (See Section 8.6.) (b) What is the magnitude of its angular momentum? Treat the ball as a thin, spherical shell. (See Section 8.7.)
A constant net torque is applied to an object. Which one of the following will not be constant? (a) angular acceleration, (b) angular velocity, (c) moment of inertia, or (d) center of gravity.
A cylinder with moment of inertia I1 rotates with angular velocity 0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not. rotating, drops onto the first cylinder (Fig. P8.73). Because the surfaces are rough, the two cylinders eventually reach the same angular speed . (a) Calculate . (b) Show that kinetic energy is lost in this situation, and calculate the ratio of the final lo the initial kinetic energy. Figure P8.73
Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
Two astronauts (Fig. P8.80), each haring a mass of 75.0 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 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. 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? (d) What are their new speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81