1 Physics And Measurement 2 Motion In One Dimension 3 Vectors 4 Motion In Two Dimensions 5 The Laws Of Motion 6 Circular Motion And Other Applications Of Newton’s Laws 7 Energy Of A System 8 Conservation Of Energy 9 Linear Momentum And Collisions 10 Rotation Of A Rigid Object About A Fixed Axis 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Universal Gravitation 14 Fluid Mechanics 15 Oscillatory Motion 16 Wave Motion 17 Sound Waves 18 Superposition And Standing Waves 19 Temperature 20 The First Law Of Thermodynamics 21 The Kinetic Theory Of Gases 22 Heat Engines, Entropy, And The Second Law Of Thermodynamics 23 Electric Fields 24 Gauss’s Law 25 Electric Potential 26 Capacitance And Dielectrics 27 Current And Resistance 28 Direct-current Circuits 29 Magnetic Fields 30 Sources Of The Magnetic Field 31 Faraday’s Law 32 Inductance 33 Alternating Current Circuits 34 Electromagnetic Waves 35 The Nature Of Light And The Principles Of Ray Optics 36 Image Formation 37 Wave Optics 38 Diffraction Patterns And Polarization 39 Relativity Chapter10: Rotation Of A Rigid Object About A Fixed Axis
Chapter Questions Section: Chapter Questions
Problem 10.1QQ: A rigid object rotates in a counterclockwise sense around a fixed axis. Each of the following pairs... Problem 10.2QQ: Consider again the pairs of angular positions for the rigid object in Quick. Quiz 10.1. If the... Problem 10.3QQ: Ethan and Rebecca are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the... Problem 10.4QQ: (i) If you are trying to loosen a stubborn screw front a piece of wood with a screwdriver and fail,... Problem 10.5QQ: You turn off your electric drill and find that the time interval for the rotating bit to come to... Problem 10.6QQ: A section of hollow pipe and a solid cylinder have the same radius, mass, and length. They both... Problem 10.7QQ: A ball rolls without slipping down incline A, starting from rest. At the same time, a box starts... Problem 10.1OQ: A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. A piece of plastic on the... Problem 10.2OQ: Consider an object on a rotating disk a distance r from its center, held in place on the disk by... Problem 10.3OQ: A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different... Problem 10.4OQ: A grindstone increases in angular speed from 4.00 rad/s to 12.00 rad/s in 4.00 s. Through what angle... Problem 10.5OQ: Suppose a cars standard tires are replaced with tires 1.30 times larger in diameter. (i) Will the... Problem 10.6OQ: Figure OQ10.6 shows a system of four particles joined by light, rigid rods. Assume a = b and M is... Problem 10.7OQ: As shown in Figure OQ10.7, a cord is wrapped onto a cylindrical reel mounted on a fixed, friction... Problem 10.8OQ: A constant net torque is exerted on an object. Which of the following quantities for the object... Problem 10.9OQ Problem 10.10OQ: A toy airplane hangs from the ceiling at the bottom end of a string. Yon turn the airplane many... Problem 10.11OQ: A solid aluminum sphere of radius R has moment of inertia I about an axis through its center. Will... Problem 10.1CQ: Is it possible to change the translational kinetic energy of an object without changing its... Problem 10.2CQ: Must an object be rotating to have a nonzero moment of inertia? Problem 10.3CQ: Suppose just two external forces act on a stationary, rigid object and the two forces are equal in... Problem 10.4CQ: Explain how you might use the apparatus described in Figure OQ10.7 to determine the moment of... Problem 10.5CQ: Example 10.6 Angular Acceleration of a Wheel A wheel of radius R mass M and moment of inertia I is... Problem 10.6CQ: Explain why changing the axis of rotation of an object changes it s moment of inertia. Problem 10.7CQ: Suppose you have two eggs, one hard-boiled and the other uncooked. You wish to determine which is... Problem 10.8CQ: Suppose you set your textbook sliding across a gymnasium floor with a certain initial speed. It... Problem 10.9CQ: (a) What is the angular speed of the second hand of an analog clock? (b) What is the direction of ... Problem 10.10CQ: One blade of a pair of scissors rotates counterclockwise in the xy plane. (a) What is the direction... Problem 10.11CQ: If you see an object rotating, is there necessarily a net torque acting on it? Problem 10.12CQ: If a small sphere of mass M were placed at the end of the rod in Figure 10.21, would the result for ... Problem 10.13CQ: Three objects of uniform densitya solid sphere, a solid cylinder, and a hollow cylinderare placed at... Problem 10.14CQ: Which of the entries in Table 10.2 applies to finding the moment of inertia (a) of a long, straight... Problem 10.15CQ: Figure CQ10.15 shows a side view of a childs tricycle with rubber tires on a horizontal concrete... Problem 10.16CQ: A person balances a meterstick in a horizontal position on the extended index fingers of her right... Problem 10.1P: (a) Find the angular speed of the Earths rotation about its axis. (b) How does this rotation affect... Problem 10.2P: A potters wheel moves uniformly from rest to an angular speed of 1.00 rev/s in 30.0 s. (a) Find its... Problem 10.3P: During a certain time interval, the angular position of a swinging door is described by = 5.00 +... Problem 10.4P: A bar on a hinge starts from rest and rotates with an angular acceleration = 10 + 6t, where is in... Problem 10.5P: A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of... Problem 10.6P: A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min. When switched... Problem 10.7P: An electric motor rotating a workshop grinding wheel at 1.00 X 102 rev/min is switched off. Assume... Problem 10.8P: A machine part rotates at an angular speed of 0.060 rad/s; its speed is then increased to 2.2 rad/s... Problem 10.9P: A dentists drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate... Problem 10.10P: Why is the following situation impossible? Starting from rest, a disk rotates around a fixed axis... Problem 10.11P: A rotating wheel requires 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of... Problem 10.12P: The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily... Problem 10.13P: A spinning wheel is slowed down by a brake, giving it a constant angular acceleration of 5.60... Problem 10.14P: Review. Consider a tall building located on the Earths equator. As the Earth rotates, a person on... Problem 10.15P: A racing car travels on a circular track of radius 250 m. Assuming the car moves with a constant... Problem 10.16P: Make an order-of-magnitude estimate of the number of revolutions through which a typical automobile... Problem 10.17P: A discus thrower (Fig. P10.9) accelerates a discus from rest to a speed of 25.0 m/s by whirling it... Problem 10.18P: Figure P10.18 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal... Problem 10.19P: A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a... Problem 10.20P: A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. Assuming the... Problem 10.21P: A disk 8.00 cm in radius rotates at a constant rate of 1 200 rev/min about its central axis.... Problem 10.22P Problem 10.23P: A car traveling on a flat (unbanked), circular track accelerates uniformly from rest with a... Problem 10.24P: A car traveling on a flat (unbanked), circular track accelerates uniformly from rest with a... Problem 10.25P: In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it.... Problem 10.26P: Review. A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50... Problem 10.27P: Find the net torque on the wheel in Figure P10.14 about the axle through O, taking a = 10.0 cm and b... Problem 10.28P: The fishing pole in Figure P10.28 makes an angle of 20.0 with the horizontal. What is the torque... Problem 10.29P: An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a... Problem 10.30P: A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It... Problem 10.31P: A 150-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in... Problem 10.32P: Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless... Problem 10.33P: A model airplane with mass 0.750 kg is tethered to the ground by a wire so that it flies in a... Problem 10.34P: A disk having moment of inertia 100 kg m2 is free to rotate without friction, starting from rest,... Problem 10.35P: The combination of an applied force and a friction force produces a constant total torque of 36.0 N ... Problem 10.36P: Review. Consider the system shown in Figure P10.36 with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and... Problem 10.37P: A potters wheela thick stone disk of radius 0.500 m and mass 100 kgis freely rotating at 50.0... Problem 10.38P: Imagine that you stand tall and turn about a vertical axis through the lop of your head and the... Problem 10.39P: A uniform, thin, solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. (a) Find its moment... Problem 10.40P: Two balls with masses M and m are connected by a rigid rod of length L, and negligible mass as shown... Problem 10.41P: Figure P10.41 shows a side view of a car tire before it is mounted on a wheel. Model it as having... Problem 10.42P: Following the procedure used in Example 10.7, prove that the moment of inertia about the y axis of... Problem 10.43P: Three identical thin rods, each of length L and mass m, are welded perpendicular to one another as... Problem 10.44P: Rigid rods of negligible mass lying along the y axis connect three panicles (Fig. P10.25). The... Problem 10.45P: The four particles in Figure P10.45 are connected by rigid rods of negligible mass. The origin is at... Problem 10.46P: Many machines employ cams for various purposes, such as opening and closing valves. In Figure... Problem 10.47P: A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now... Problem 10.48P: A horizontal 800-N merry-go-round is a solid disk of radius 1.50 m and is started from rest by a... Problem 10.49P: Big Ben, the nickname for the clock in Elizabeth Tower (named after the Queen in 2012) in London,... Problem 10.50P: Consider two objects with m1 m2 connected by a light string that passes over a pulley having a... Problem 10.51P: The top in Figure P10.51 has a moment of inertia of 4.00 104 kg m2 and is initially at rest. It is... Problem 10.52P: Why is the following situation impossible? In a large city with an air-pollution problem, a bus has... Problem 10.53P: In Figure P10.53, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass m2 =... Problem 10.54P: Review. A thin, cylindrical rod = 24.0 cm long with mass m = 1.20 kg has a ball of diameter d =... Problem 10.55P: Review. An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped... Problem 10.56P: This problem describes one experimental method for determining the moment of inertia of an... Problem 10.57P: A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a... Problem 10.58P: The head of a grass string trimmer has 100 g of cord wound in a light, cylindrical spool with inside... Problem 10.59P: A cylinder of mass 10.0 kg rolls without slipping on a horizontal surface. At a certain instant, its... Problem 10.60P: A solid sphere is released from height h from the top of an incline making an angle with the... Problem 10.61P: (a) Determine the acceleration of the center of mass of a uniform solid disk rolling down an incline... Problem 10.62P: A smooth cube of mass m and edge length r slides with speed v non a horizontal surface with... Problem 10.63P: A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height... Problem 10.64P: A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on... Problem 10.65P: A metal can containing condensed mushroom soup has mass 215 g, height 10.8 cm, and diameter 6.38 cm.... Problem 10.66AP: As shown in Figure 10.13 on page 306, toppling chimneys often break apart in midfall because the... Problem 10.67AP: Review. A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius... Problem 10.68AP: An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by... Problem 10.69AP: A shaft is turning at 65.0 rad/s at time t = 0. Thereafter, its angular acceleration is given by... Problem 10.70AP: A shaft is turning at angular speed at time t = 0. Thereafter, its angular acceleration is given by... Problem 10.71AP: Review. A mixing beater consists of three thin rods, each 10.0 cm long. The rods diverge from a... Problem 10.72AP: The hour hand and the minute hand of Big Ben, the Elizabeth Tower clock in London, are 2.70 m and... Problem 10.73AP: A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through... Problem 10.74AP: A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend... Problem 10.75AP: A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend... Problem 10.76AP Problem 10.77AP: Review. As shown in Figure P10.77, two blocks are connected by a string of negligible mass passing... Problem 10.78AP: Review. A string is wound around a uniform disk of radius R and mass M. The disk is released from... Problem 10.79AP: The reel shown in Figure P10.79 has radius R and moment of inertia I. One end of the block of mass m... Problem 10.80AP: A common demonstration, illustrated in Figure P10.80, consists of a ball resting at one end of a... Problem 10.81AP: A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with... Problem 10.82AP: Review. A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.42).... Problem 10.83AP: A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.8S.... Problem 10.84AP: A thin rod of mass 0.630 kg and length 1.24 m is at rest, hanging vertically from a strong, fixed... Problem 10.85AP Problem 10.86AP: Review. A clown balances a small spherical grape at the top of his bald head, which also has the... Problem 10.87CP: A plank with a mass M = 6.00 kg rests on top of two identical, solid, cylindrical rollers that have... Problem 10.88CP: As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel... Problem 10.89CP: As a result of friction, the angular speed of a whorl changes with time according to ddt=et where 0... Problem 10.90CP: To find the total angular displacement during the playing time of the compact disc in part (B) of... Problem 10.91CP: A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as depicted in the... Problem 10.92CP: A cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cords free... Problem 10.93CP: A merry-go-round is stationary. A clog is running around the merry-go-round on the ground just... Problem 10.94CP: A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig.... Problem 10.7OQ: As shown in Figure OQ10.7, a cord is wrapped onto a cylindrical reel mounted on a fixed, friction...
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A 25.00 m long nylon rope is wound around a bobbin with a radius of 0.75 m and a mass of 2.50 kg. The bobbin is placed on a frictionless axis and has an initial angular velocity of 1.5 rad/s. The rope is started to be pulled from the bobbin with a constant angular acceleration of 3.50 m/s2. How much work has been done on the bobbin when it reaches 12 rad/s?
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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