A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speedof 15.0 m/s.(a) Determine the translational kinetic energy of its center of mass.J(b) Determine the rotational kinetic energy about its center of mass.J(c) Determine its total energy.J

key concept mass of center of mass=mass of objecttranslational kinetic energy of an object = 1/2…

Answered: A cylinder of mass 8.0 kg rolls without…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 63PQ: A uniform cylinder of radius r = 10.0 cm and mass m = 2.00 kg is rolling without slipping on a...

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A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?
A wad of sticky clay with mass m and velocity vi is fired at a solid cylinder of mass M and radius R (Fig. P10.75). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d R from the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is the mechanical energy of the claycylinder system constant in this process? Explain your answer. (c) Is the momentum of the claycylinder system constant in this process? Explain your answer. Figure P10.75
A uniform cylinder of radius r = 10.0 cm and mass m = 2.00 kg is rolling without slipping on a horizontaltabletop. The cylinders center ofmass is observed to have a speed of 5.00 m/s at a given instant. a. What isthe translational kinetic energy of thecylinder at that instant? b. What is therotational kinetic energy of the cylinder around its center of mass at thatinstant? c. What is the total kineticenergy of the cylinder at that instant?
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.
A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to the rod with an angularspeed of 3.00 rad/s. a. What is the angular momentum of therod if the axis passes through the rods midpoint? b. What is theangular momentum of the rod if the axis passes through a pointhalfway between its midpoint and its end?
Consider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.44. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.
A uniform cylindrical grinding wheel of mass 50.0 kg and diameter 1.0 m is turned on by an electric motor. The friction in the bearings is negligible. (a) What torque must be applied to the wheel to bring it from rest to 120 rev/min in 20 revolutions? (b) A tool whose coefficent of kinetic friction with the wheel with a force of 40.0 N. What torque must be supplied by the motor to keep the wheel rotating at a constant angular velocity?
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 propeller consists of two blades each 3.0 m in length and mass 120 kg each. The propeller can be approximated by a single rod rotating about its center of mass. The propeller starts from rest and rotates up to 1200 rpm in 30 seconds at a constant rate. (a) What is the angular momentum of the propeller at t=10s ; t=20s ? (b) What is the torque on the propeller?
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.
Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75
While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900kg-m2 the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0° with a constant force exerted by the muscle?

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