University Physics Volume 1 18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: William Moebs, Samuel J. Ling, Jeff Sanny
1 Units And Measurement 2 Vectors 3 Motion Along A Straight Line 4 Motion In Two And Three Dimensions 5 Newton's Law Of Motion 6 Applications Of Newton's Laws 7 Work And Kinetic Energy 8 Potential Energy And Conservation Of Energy 9 Linear Momentum And Collisions 10 Fixed-axis Rotation 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Gravitation 14 Fluid Mechanics 15 Oscillations 16 Waves 17 Sound Chapter11: Angular Momentum
Chapter Questions Section: Chapter Questions
Problem 11.1CYU: Check Your Understanding A hollow cylinder is on an incline at an angle of 60 . The coefficient of... Problem 11.2CYU: Check Your Understanding A proton spiraling around a magnetic field executes circular motion in the... Problem 11.3CYU: Check Your Understanding Which has greater angular momentum: a solid sphere of mass m rotating at a... Problem 11.4CYU: Check Your Understanding A merry-go-round at a playground is rotating at 4.0 rev/min. Three children... Problem 11.5CYU: Check Your Understanding A top has a precession frequency of 5.0 rad/s on Earth. What is its... Problem 1CQ: Can a round object released from rest at the top of a frictionless incline undergo rolling motion? Problem 2CQ: A cylindrical can of radius R is rolling across a horizontal surface without slipping. (a) After one... Problem 3CQ: A wheel is released from the top on an incline. Is the wheel most likely to slip if the incline is... Problem 4CQ: Which rolls down an inclined plane faster, a hollow cylinder or a solid sphere? Both have the same... Problem 5CQ: A hollow sphere and a hollow cylinder of the same radius and mass roll up an incline without... Problem 6CQ: Can you assign an angular momentum to a particle without first defining a reference point? Problem 7CQ: For a particle traveling in a straight line, are there any points about which the angular momentum... Problem 8CQ: Under what conditions does a rigid body have angular momentum but not linear momentum? Problem 9CQ: If a particle is moving with respect to a chosen origin it has linear momentum. What conditions must... Problem 10CQ: If you know the velocity of a particle, can you say anything about the particle’s angular momentum? Problem 11CQ: What is the purpose of the small propeller at the back of a helicopter that rotates in the plane... Problem 12CQ: Suppose a child walks from the outer edge of a rotating merry-go-round to the inside. Does the... Problem 13CQ: As the rope of a tethered ball winds around a pole, what happens to the angular velocity of the... Problem 14CQ: Suppose the polar ice sheets broke free and floated toward Earth’s equator without melting. What... Problem 15CQ: Explain why stars spin faster when they collapse. Problem 16CQ: Competitive divers pull their limbs in and curl up their bodies when they do flips. Just before... Problem 17CQ: Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum... Problem 18CQ: Earth precesses about its vertical axis with a period of 26,000 years. Discuss whether Equation... Problem 19P: What is the angular velocity of a 75.0-cm-diameter tire on an automobile traveling at 90.0 km/h? Problem 20P: A boy rides his bicycle 2.00 km. The wheels have radius 30.0 cm. What is the total angle the tires... Problem 21P: If the boy on the bicycle in the preceding problem accelerates from rest to a speed of 10.0 m/s in... Problem 22P: Formula One race cars have 66-cm-diameter tires. If a Formula One averages a speed of 300 km/h... Problem 23P: A marble rolls down an incline at 30 from rest. (a) What is its acceleration? (b) How far does it go... Problem 24P: Repeat the preceding problem replacing the marble with a solid cylinder. Explain the new result. Problem 25P: A rigid body with a cylindrical cross-section is released from the top of a 30 incline. It rolls... Problem 26P: A yo-yo can be thought of a solid cylinder of mass m and radius r that has a light string wrapped... Problem 27P: A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is... Problem 28P: A bowling ball rolls up a ramp 0.5 m high without slipping to storage. It has an initial velocity of... Problem 29P: A 40.0-kg solid cylinder is rolling across a horizontal surface at a speed of 6.0 m/s. How much work... Problem 30P: A 40.0-kg solid sphere is rolling across a horizontal surface with a speed of 6.0 m/s. How much work... Problem 31P: A solid cylinder rolls up an incline at an angle of 20 . If it starts at the bottom with a speed of... Problem 32P: A solid cylindrical wheel of mass M and radius R is pulled by a force applied to the center of the... Problem 33P: A hollow cylinder that is rolling without slipping is given a velocity of 5.0 m/s and rolls up an... Problem 34P: A 0.2-kg particle is travelling along the line y=2.0m with a velocity 5.0 m/s. What is the angular... Problem 35P: A bird flies overhead from where you stand at an altitude of 300.0 m and at a speed horizontal to... Problem 36P: A Formula One race car with mass 750.0 kg is speeding through a course in Monaco and enters a... Problem 37P: A particle of mass 5.0 kg has position vector at a particular instant of time when its velocity is... Problem 38P: Use the right-hand rule to determine the directions of the angular momenta about the origin of the... Problem 39P: Suppose the particles in the preceding problem have masses m1=0.10kg , m2=0.20kg , m3=0.30kg ,... Problem 40P: Two particles of equal mass travel with the same speed in opposite directions along parallel lines... Problem 41P: An airplane of mass 4.0104kg flies horizontally at an altitude of 10 km with a constant speed of 250... Problem 42P: At a particular instant, a 1.0-kg particle’s position is , its velocity is , and the force on it is... Problem 43P Problem 44P: (a) Calculate the angular momentum of Earth in its orbit around the Sun. (b) Compare this angular... Problem 45P: A boulder of mass 20 kg and radius 20 cm rolls down a hill 15 m high from rest. What is its angular... Problem 46P: A satellite is spinning at 6.0 rev/s. The satellite consists of a main body in the shape of a sphere... Problem 47P: A propeller consists of two blades each 3.0 m in length and mass 120 kg each. The propeller can be... Problem 48P: A pulsar is a rapidly rotating neutron star. The Crab nebula pulsar in the constellation Taurus has... Problem 49P: The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min.... Problem 50P: A roller coaster has mass 3000.0 kg and needs to make it safely through a vertical circular loop of... Problem 51P: A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0... Problem 52P: Conservation of Angular Momentum 52.A disk of mass 2.0 kg and radius 60 cm with a small mass of 0.05... Problem 53P: The Sun’s mass is 2.01030kg , its radius is 7.0105km , and it has a rotational period of... Problem 54P: A cylinder with rotational inertia I1=2.0kgm2 rotates clockwise about a vertical axis through its... Problem 55P: A diver off the high board imparts an initial rotation with his body fully extended before going... Problem 56P: An Earth satellite has its apogee at 2500 km above the surface of Earth and perigee at 500 km above... Problem 57P: A Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous... Problem 58P: Shown below is a small particle of mass 20 g that is moving at a speed of 10.0 m/s when it collides... Problem 59P: A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M=0.10kg,R=0.10m)... Problem 60P: A uniform rod of mass 200 g and length 100 cm is free to rotate in a horizontal plane around a fixed... Problem 61P: A merry-go-round has a radius of 2.0 m and a moment of inertia 300kgm2 . A boy of mass 50 kg runs... Problem 62P: A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an... Problem 63P: Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and... Problem 64P: (a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of... Problem 65P: Twin skaters approach one another as shown below and lock hands. (a) Calculate their final angular... Problem 66P: A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The... Problem 67P: In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the... Problem 68P: A satellite in a geosynchronous circular orbit is 42,164.0 km from the center of Earth. A small... Problem 69P: A gymnast does cartwheels along the floor and then launches herself into the air and executes... Problem 70P: The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce farces on its... Problem 71P: A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes... Problem 72P: An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is... Problem 73P: A space station consists of a giant rotating hollow cylinder of mass 106kg including people on the... Problem 74P: Neptune has a mass of 1.01026kg and is 4.5109km from the Sun with an orbital period of 165 years.... Problem 75P: A gyroscope has a 0.5-kg disk that spins at 40 rev/s. The center of mass of the disk is 10 cm from a... Problem 76P: The precession angular velocity of a gyroscope is 1.0 rad/s. If the mass of the rotating disk is 0.4... Problem 77P: The axis of Earth makes a 23.5 angle with a direction perpendicular to the plane of Earth’s orbit.... Problem 78AP: A marble is rolling across the floor at a speed of 7.0 m/s when it starts up a plane inclined at 30... Problem 79AP: Repeat the preceding problem replacing the marble with a hollow sphere. Explain the new results. Problem 80AP: The mass of a hoop of radius 1.0 m is 6.0 kg. It rolls across a horizontal surface with a speed of... Problem 81AP: Repeat the preceding problem for a hollow sphere of the same radius and mass and initial speed.... Problem 82AP: A particle has mass 0.5 kg and is traveling along the line x=5.0m at 2.0 m/s In the positive... Problem 83AP: A 4.0-kg particle moves in a circle of radius 2.0 m. The angular momentum of the particle varies in... Problem 84AP: A proton is accelerated in a cyclotron to 5.0106m/s in 0.01 s. The proton follows a circular path.... Problem 85AP: (a) What is the angular momentum of the Moon in its orbit around Earth? (b) How does this angular... Problem 86AP: A DVD is rotating at 500 rpm. What is the angular momentum of the DVD if has a radius of 6.0 cm and... Problem 87AP: A potter’s disk spins from rest up to 10 rev/s in 15 s. The disk has a mass 3.0 kg and radius 30.0... Problem 88AP: Suppose you start an antique car by exerting a force of 300 N on its crank for 0.250 s. What is the... Problem 89AP: A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis... Problem 90AP: A boy stands at the center of a platform that is rotating without friction at 1.0 rev/s. The boy... Problem 91AP: Eight children each of mass 40 kg, climb on a small merry-go-round. They position themselves evenly... Problem 92AP: A thin meter stick of mass 150 g rotates around an axis perpendicular to the stick’s long axis at an... Problem 93AP: A satellite in the shape of a sphere of mass 20,000 kg and radius 5.0 m is spinning about an axis... Problem 94AP: A top has moment of inertia 3.2104kgm2 and radius 4.0 cm from the center of mass to the pivot point.... Problem 95CP: The truck shown below is initially at rest with solid cylindrical roll of paper sitting on its bed.... Problem 96CP: A bowling ball of radius 8.5 cm is tossed onto a bowling lane with speed 9.0 m/s. The direction of... Problem 97CP: A small ball of mass 0.50 kg is attached by a massless sting to a vertical rod that Is spinning as... Problem 98CP: A bug flying horizontally at 1.0 m/s collides and sticks to the end of a uniform stick hanging... Problem 49P: The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min....
Related questions
Concept explainers
b. At the bottom of the ramp, compare (using <, > and/or =) the object’s rotational kinetic energy with its angular momentum to the magnitude
*I only need b and c. Also please write a detail as much as possible.
Transcribed Image Text: b. At the bottom of the ramp, compare (using <, > and/or =) the object's rotational kinetic energy with its
translational kinetic energy.
_Krot
At the bottom of the ramp, find the ratio of the magnitude of the object's angular momentum to the magnitude
Kerans
С.
of its linear momentum.
Lpottem
Pbottom
Transcribed Image Text: In order for an object to roll smoothly (with constant angular acceleration) down a ramp, it must have either spherical or
cylindrical symmetry. Consider spherically and cylindrically symmetric objects with mass M and outer radius R rolling
without slipping down an incline of height h and angle 0 from the horizontal. The rotational inertias of such objects can
be written in the generalized form: I = CMR², where c is a shape factor whose value depends on the geometry of the
object. (If you look at the table of rotational inertias in the textbook you'll be able to see that this is true.)
(For this question, consider M, R, c, h, 0, and g as the given quantities –express your answers in terms of some or
all of these quantities. Simplify your answers as much as you can.)
a.
If the object starts from rest at the very top of the ramp before rolling freely down
the ramp without slipping, find the objecť's (linear) speed at the bottom of the ramp.
(Hint: use conservation of energy.)
Vpottom
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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