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 Superposition And Standing Waves 18 Temperature 19 The First Law Of Thermodynamics 20 The Kinetic Theory Of Gases 21 Heat Engines, Entropy, And The Second Law Of Thermodynamics 22 Electricity And Magnetism 23 Continuous Charge Distributions And Gauss's Law 24 Electric Potential 25 Capacitance And Dielectrics 26 Current And Resistance 27 Direct-current Circuits 28 Magnetic Fields 29 Sources Of The Magnetic Field 30 Faraday's Law 31 Inductance 32 Alternating-current Circuits 33 Electromagnetic Waves 34 The Nature Of Light And The Principles Of Ray Optics 35 Image Fonnation 36 Wave Optics 37 Diffraction Patterns And Polarization 38 Relativity Chapter10: Rotation Of A Rigid Object About A Fixed Axis
10.1 Angular Position, Velocity, And Acceleration 10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration 10.3 Angular And Translational Quantities 10.4 Torque 10.5 Analysis Model: Rigid Object Under A Net Torque 10.6 Calculation Of Moments Of Inertia 10.7 Rotational Kinetic Energy 10.8 Energy Considerations In Rotational Motion 10.9 Rolling Motion Of A Right Object Chapter Questions Section: Chapter Questions
Problem 1P: (a) Find the angular speed of the Earths rotation about its axis. (b) How does this rotation affect... Problem 2P: A bar on a hinge starts from rest and rotates with an angular acceleration = 10 + 6t, where is in... Problem 3P: A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of... Problem 4P: A machine part rotates at an angular speed of 0.060 rad/s; its speed is then increased to 2.2 rad/s... Problem 5P: A dentists drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate... Problem 6P: Why is the following situation impossible? Starting from rest, a disk rotates around a fixed axis... Problem 7P: Review. Consider a tall building located on the Earths equator. As the Earth rotates, a person on... Problem 8P: Make an order-of-magnitude estimate of the number of revolutions through which a typical automobile... Problem 9P: A discus thrower (Fig. P10.9) accelerates a discus from rest to a speed of 25.0 m/s by whirling it... Problem 10P Problem 11P: A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. Assuming the... Problem 12P: Review. A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50... Problem 13P: In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it.... Problem 14P: Find the net torque on the wheel in Figure P10.14 about the axle through O, taking a = 10.0 cm and b... Problem 15P: A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It... Problem 16P: Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless... Problem 17P: A model airplane with mass 0.750 kg is tethered to the ground by a wire so that it flies in a... Problem 18P: A disk having moment of inertia 100 kg m2 is free to rotate without friction, starting from rest,... Problem 19P: Your grandmother enjoys creating pottery as a hobby. She uses a potters wheel, which is a stone disk... Problem 20P: At a local mine, a cave-in has trapped a number of miners. You and some classmates rush to the scene... Problem 21P: You have just bought a new bicycle. On your first riding trip, it seems that the hike comes to rest... Problem 22P: Imagine that you stand tall and turn about a vertical axis through the lop of your head and the... Problem 23P: Following the procedure used in Example 10.7, prove that the moment of inertia about the y axis of... Problem 24P: Two balls with masses M and m are connected by a rigid rod of length L, and negligible mass as shown... Problem 25P: Rigid rods of negligible mass lying along the y axis connect three panicles (Fig. P10.25). The... Problem 26P: A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now... Problem 27P: Big Ben, the nickname for the clock in Elizabeth Tower (named after the Queen in 2012) in London,... Problem 28P: Consider two objects with m1 m2 connected by a light string that passes over a pulley having a... Problem 29P: Review. An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped... Problem 30P: Why is the following situation impossible? In a large city with an air-pollution problem, a bus has... Problem 31P: A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a... Problem 32P: This problem describes one experimental method for determining the moment of inertia of an... Problem 33P: A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on... Problem 34P: A smooth cube of mass m and edge length r slides with speed v non a horizontal surface with... Problem 35P: A metal can containing condensed mushroom soup has mass 215 g, height 10.8 cm, and diameter 6.38 cm.... Problem 36AP: You have been hired as an expert witness in the case of a factory owner suing a demolition company.... Problem 37AP: A shaft is turning at 65.0 rad/s at time t = 0. Thereafter, its angular acceleration is given by... Problem 38AP: A shaft is turning at angular speed at time t = 0. Thereafter, its angular acceleration is given by... Problem 39AP: An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by... Problem 40AP: The hour hand and the minute hand of Big Ben, the Elizabeth Tower clock in London, are 2.70 m and... Problem 41AP: Review. A string is wound around a uniform disk of radius R and mass M. The disk is released from... Problem 42AP: Review. A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.42).... Problem 43AP: Review. A clown balances a small spherical grape at the top of his bald head, which also has the... Problem 44CP: As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel... Problem 45CP: A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as depicted in the... Problem 46CP: To find the total angular displacement during the playing time of the compact disc in part (B) of... Problem 47CP: A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig.... Problem 48CP: A cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cords free... Problem 37AP: A shaft is turning at 65.0 rad/s at time t = 0. Thereafter, its angular acceleration is given by...
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37. A motor starts rotating from rest with an angular acceleration of 12 rad/s2. What is the motor’s angular velocity 4 s later?
d. 48 rad/s
Explanation and solution
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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