3. A 5.20-kilogram hoop starts from rest at a height 1.30 m above the base of an inclined plane and rolls down under the influence of gravity. What is thelinear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.)m/s

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Answered: 3. A 5.20-kilogram hoop starts from…

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 15OQ

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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 buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?
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A solid, uniform disk of radius 0.250 m and mass 55.0 kg rolls down a ramp of length 4.50 m that makes an angle of 15.0 with the horizontal. The disk starts from rest from the top of the ramp. Find (a) the speed of the disks center of mass when it reaches the bottom of the ramp and (b) the angular speed of the disk at the bottom of the ramp.
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?
Review. A projectile of mass m is launched with an initial velocity vi making an angle with the horizontal as shown in Figure P11.11. The projectile moves in the gravitational field of the Earth. Find the angular momentum of the projectile about the origin (a) when the projectile is at the origin, (b) when it is at the highest point of its trajectory, and (c) just before it hits the ground. (d) What torque causes its angular momentum to change? Figure P11.11
A 5.50-kilogram hoop starts from rest at a height 1.30 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.)
A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp?
A 78.0 kg hoop rolls along a horizontal floor so that its center of mass has a speed of 0.0720 m/s. How much work must be done on the hoop to stop it?
A thin cylindrical shell of M = 4.00 kg and radius R = 2.50 m is rollingdown an inclide. If it is released from rest at the top of the incline of h=9.00m, what is the speed of the center of mass of the cylindrical shell at the bottom of the incline? (?ℎ? ?????? ?? ??????? ?? ? ??????????? ?ℎ???: ? = ??^2)

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3. A 5.20-kilogram hoop starts from rest at a height 1.30 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.) m/s