1 Getting Started 2 One Dimensional Motion 3 Vectors 4 Two-and-three Dimensional Motion 5 Newton's Laws Of Motion 6 Applications Of Newton’s Laws Of Motion 7 Gravity 8 Conservation Of Energy 9 Energy In Nonisolated Systems 10 Systems Of Particles And Conservation Of Momentum 11 Collisions 12 Rotation I: Kinematics And Dynamics 13 Rotation Ii: A Conservation Approach 14 Static Equilibrium, Elasticity, And Fracture 15 Fluids 16 Oscillations 17 Traveling Waves 18 Superposition And Standing Waves 19 Temperature, Thermal Expansion And Gas Laws 20 Kinetic Theory Of Gases 21 Heat And The First Law Of Thermodynamics 22 Entropy And The Second Law Of Thermodynamics 23 Electric Forces 24 Electric Fields 25 Gauss’s Law 26 Electric Potential 27 Capacitors And Batteries 28 Current And Resistance 29 Direct Current (dc) Circuits 30 Magnetic Fields And Forces 31 Gauss’s Law For Magnetism And Ampère’s Law 32 Faraday’s Law Of Induction 33 Inductors And Ac Circuits 34 Maxwell’s Equations And Electromagnetic Waves 35 Diffraction And Interference 36 Applications Of The Wave Model 37 Reflection And Images Formed By Reflection 38 Refraction And Images Formed By Refraction 39 Relativity Chapter13: Rotation Ii: A Conservation Approach
13.1 Conservation Approach 13.2 Rotational Inertia 13.3 Rotational Kinetic Energy 13.4 Special Case Of Rolling Motion 13.5 Work And Power 13.6 Angular Momentum 13.7 Conservation Of Angular Momentum Chapter Questions Section: Chapter Questions
Problem 1PQ Problem 2PQ Problem 3PQ: A Frisbee flies across a field. Determine if the system has translational kinetic energy, rotational... Problem 4PQ Problem 5PQ Problem 6PQ: Rotational Inertia Problems 5 and 6 are paired. 5. N A system consists of four boxes modeled as... Problem 7PQ: A 12.0-kg solid sphere of radius 1.50 m is being rotated by applying a constant tangential force of... Problem 8PQ: A figure skater clasps her hands above her head as she begins to spin around a vertical axis that... Problem 9PQ: A solid sphere of mass M and radius Ris rotating around an axis that is tangent tothe sphere (Fig.... Problem 10PQ: Suppose a disk having massMtot and radius R is broken intofour equal parts (Fig. P13.10).What is the... Problem 11PQ: Problems 11 and 12 are paired. A thin disk of radius R has a nonuniform density = 4.5r2, when r is... Problem 12PQ: Given the disk and density in Problem 11, derive an expression for the rotational inertia of this... Problem 13PQ: A large stone disk is viewed from above and is initially at restas seen in Figure P13.13. The disk... Problem 14PQ Problem 15PQ: A uniform disk of mass M = 3.00 kg and radius r = 22.0 cm is mounted on a motor through its center.... Problem 16PQ Problem 17PQ Problem 18PQ: The system shown in Figure P13.18 consisting of four particles connected by massless, rigid rods is... Problem 19PQ: A 10.0-kg disk of radius 2.0 m rotates from rest as a result of a 20.0-N tangential forceapplied at... Problem 20PQ Problem 21PQ Problem 22PQ: In Problem 21, what fraction of the kinetic energy is translational kinetic energy, and what... Problem 23PQ Problem 24PQ Problem 25PQ Problem 26PQ: A student amuses herself byspinning her pen around her thumb(Fig. P13.26). Estimate the rotational... Problem 27PQ: The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis... Problem 28PQ Problem 29PQ Problem 30PQ Problem 31PQ: Sophia is playing with a set of wooden toys, rolling them offthe table and onto the floor. One of... Problem 32PQ Problem 33PQ: A spring with spring constant 25 N/m is compressed a distance of 7.0 cm by a ball with a mass of... Problem 34PQ Problem 35PQ Problem 36PQ Problem 37PQ Problem 38PQ Problem 39PQ: A parent exerts a torque on a merry-go-round at a park. The torque has a magnitude given by... Problem 40PQ Problem 41PQ: Today, waterwheels are not often used to grind food. Instead, we have electrical devices such as... Problem 42PQ Problem 43PQ: A buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal... Problem 44PQ: An object of mass M isthrown with a velocity v0 at anangle with respect to thehorizontal (Fig.... Problem 45PQ: 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... Problem 46PQ: 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... Problem 47PQ Problem 48PQ: Two particles of mass m1 = 2.00 kgand m2 = 5.00 kg are joined by a uniform massless rod of length =... Problem 49PQ: A turntable (disk) of radius r = 26.0 cm and rotational inertia0.400 kg m2 rotates with an angular... Problem 50PQ: CHECK and THINK Our results give us a way to think about how a person might steer a unicycle.... Problem 51PQ Problem 52PQ Problem 53PQ: Two children (m = 30.0 kg each) stand opposite each otheron the edge of a merry-go-round. The... Problem 54PQ: A disk of mass m1 is rotating freely with constant angularspeed . Another disk of mass m2 that has... Problem 55PQ Problem 56PQ Problem 57PQ: The angular momentum of a sphere is given by L=(4.59t3)i+(6.011.19t2)j+(6.26t)k , where L hasunits... Problem 58PQ Problem 59PQ Problem 60PQ Problem 61PQ Problem 62PQ Problem 63PQ: A uniform cylinder of radius r = 10.0 cm and mass m = 2.00 kg is rolling without slipping on a... Problem 64PQ Problem 65PQ: A thin, spherical shell of mass m and radius R rolls down aparabolic path PQR from height H without... Problem 66PQ: To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam... Problem 67PQ Problem 68PQ Problem 69PQ: The velocity of a particle of mass m = 2.00 kg is given by v= 5.10 + 2.40 m /s. What is the angular... Problem 70PQ: A ball of mass M = 5.00 kg and radius r = 5.00 cm isattached to one end of a thin,cylindrical rod of... Problem 71PQ: A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to... Problem 72PQ: A solid sphere and a hollow cylinder of the same mass and radius have a rolling race down an incline... Problem 73PQ: A uniform disk of mass m = 10.0 kg and radius r = 34.0 cm mounted on a frictionlessaxle through its... Problem 74PQ: When a person jumps off a diving platform, she imparts some amount of angular momentum to her body.... Problem 75PQ: One end of a massless rigid rod of length is attached to a woodenblock of mass M restingon a... Problem 76PQ: A uniform solid sphere of mass m and radius r is releasedfrom rest and rolls without slipping on a... Problem 77PQ Problem 78PQ: A cam of mass M is in the shape of a circular disk of diameter 2R with an off-center circular hole... Problem 79PQ Problem 80PQ: Consider the downhill race in Example 13.9 (page 372). The acceleration of a particle down an... Problem 81PQ Problem 69PQ: The velocity of a particle of mass m = 2.00 kg is given by v= 5.10 + 2.40 m /s. What is the angular...
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Show that the kinetic energy of an object rotating about a fixed axis with angular momentum L = Iω can be written as K = L 2 /2I .
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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