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  1. Preface
  2. Unit 1. Mechanics
    1. 1 Units and Measurement
      1. Introduction
      2. 1.1 The Scope and Scale of Physics
      3. 1.2 Units and Standards
      4. 1.3 Unit Conversion
      5. 1.4 Dimensional Analysis
      6. 1.5 Estimates and Fermi Calculations
      7. 1.6 Significant Figures
      8. 1.7 Solving Problems in Physics
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Vectors
      1. Introduction
      2. 2.1 Scalars and Vectors
      3. 2.2 Coordinate Systems and Components of a Vector
      4. 2.3 Algebra of Vectors
      5. 2.4 Products of Vectors
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 3 Motion Along a Straight Line
      1. Introduction
      2. 3.1 Position, Displacement, and Average Velocity
      3. 3.2 Instantaneous Velocity and Speed
      4. 3.3 Average and Instantaneous Acceleration
      5. 3.4 Motion with Constant Acceleration
      6. 3.5 Free Fall
      7. 3.6 Finding Velocity and Displacement from Acceleration
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Motion in Two and Three Dimensions
      1. Introduction
      2. 4.1 Displacement and Velocity Vectors
      3. 4.2 Acceleration Vector
      4. 4.3 Projectile Motion
      5. 4.4 Uniform Circular Motion
      6. 4.5 Relative Motion in One and Two Dimensions
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    5. 5 Newton's Laws of Motion
      1. Introduction
      2. 5.1 Forces
      3. 5.2 Newton's First Law
      4. 5.3 Newton's Second Law
      5. 5.4 Mass and Weight
      6. 5.5 Newton’s Third Law
      7. 5.6 Common Forces
      8. 5.7 Drawing Free-Body Diagrams
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 6 Applications of Newton's Laws
      1. Introduction
      2. 6.1 Solving Problems with Newton’s Laws
      3. 6.2 Friction
      4. 6.3 Centripetal Force
      5. 6.4 Drag Force and Terminal Speed
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 7 Work and Kinetic Energy
      1. Introduction
      2. 7.1 Work
      3. 7.2 Kinetic Energy
      4. 7.3 Work-Energy Theorem
      5. 7.4 Power
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    8. 8 Potential Energy and Conservation of Energy
      1. Introduction
      2. 8.1 Potential Energy of a System
      3. 8.2 Conservative and Non-Conservative Forces
      4. 8.3 Conservation of Energy
      5. 8.4 Potential Energy Diagrams and Stability
      6. 8.5 Sources of Energy
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    9. 9 Linear Momentum and Collisions
      1. Introduction
      2. 9.1 Linear Momentum
      3. 9.2 Impulse and Collisions
      4. 9.3 Conservation of Linear Momentum
      5. 9.4 Types of Collisions
      6. 9.5 Collisions in Multiple Dimensions
      7. 9.6 Center of Mass
      8. 9.7 Rocket Propulsion
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    10. 10 Fixed-Axis Rotation
      1. Introduction
      2. 10.1 Rotational Variables
      3. 10.2 Rotation with Constant Angular Acceleration
      4. 10.3 Relating Angular and Translational Quantities
      5. 10.4 Moment of Inertia and Rotational Kinetic Energy
      6. 10.5 Calculating Moments of Inertia
      7. 10.6 Torque
      8. 10.7 Newton’s Second Law for Rotation
      9. 10.8 Work and Power for Rotational Motion
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    11. 11 Angular Momentum
      1. Introduction
      2. 11.1 Rolling Motion
      3. 11.2 Angular Momentum
      4. 11.3 Conservation of Angular Momentum
      5. 11.4 Precession of a Gyroscope
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    12. 12 Static Equilibrium and Elasticity
      1. Introduction
      2. 12.1 Conditions for Static Equilibrium
      3. 12.2 Examples of Static Equilibrium
      4. 12.3 Stress, Strain, and Elastic Modulus
      5. 12.4 Elasticity and Plasticity
      6. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    13. 13 Gravitation
      1. Introduction
      2. 13.1 Newton's Law of Universal Gravitation
      3. 13.2 Gravitation Near Earth's Surface
      4. 13.3 Gravitational Potential Energy and Total Energy
      5. 13.4 Satellite Orbits and Energy
      6. 13.5 Kepler's Laws of Planetary Motion
      7. 13.6 Tidal Forces
      8. 13.7 Einstein's Theory of Gravity
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    14. 14 Fluid Mechanics
      1. Introduction
      2. 14.1 Fluids, Density, and Pressure
      3. 14.2 Measuring Pressure
      4. 14.3 Pascal's Principle and Hydraulics
      5. 14.4 Archimedes’ Principle and Buoyancy
      6. 14.5 Fluid Dynamics
      7. 14.6 Bernoulli’s Equation
      8. 14.7 Viscosity and Turbulence
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Waves and Acoustics
    1. 15 Oscillations
      1. Introduction
      2. 15.1 Simple Harmonic Motion
      3. 15.2 Energy in Simple Harmonic Motion
      4. 15.3 Comparing Simple Harmonic Motion and Circular Motion
      5. 15.4 Pendulums
      6. 15.5 Damped Oscillations
      7. 15.6 Forced Oscillations
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 16 Waves
      1. Introduction
      2. 16.1 Traveling Waves
      3. 16.2 Mathematics of Waves
      4. 16.3 Wave Speed on a Stretched String
      5. 16.4 Energy and Power of a Wave
      6. 16.5 Interference of Waves
      7. 16.6 Standing Waves and Resonance
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    3. 17 Sound
      1. Introduction
      2. 17.1 Sound Waves
      3. 17.2 Speed of Sound
      4. 17.3 Sound Intensity
      5. 17.4 Normal Modes of a Standing Sound Wave
      6. 17.5 Sources of Musical Sound
      7. 17.6 Beats
      8. 17.7 The Doppler Effect
      9. 17.8 Shock Waves
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
  12. Index

Check Your Understanding

10.1

a. 40.0rev/s=2π(40.0)rad/s40.0rev/s=2π(40.0)rad/s, α=ΔωΔt=2π(40.0)0rad/s20.0s=2π(2.0)=4.0πrad/s2α=ΔωΔt=2π(40.0)0rad/s20.0s=2π(2.0)=4.0πrad/s2; b. Since the angular velocity increases linearly, there has to be a constant acceleration throughout the indicated time. Therefore, the instantaneous angular acceleration at any time is the solution to 4.0πrad/s24.0πrad/s2.

10.2

a. Using Equation 10.11, we have 7000rpm=7000.0(2πrad)60.0s=733.0rad/s,7000rpm=7000.0(2πrad)60.0s=733.0rad/s,
α=ωω0t=733.0rad/s10.0s=73.3rad/s2α=ωω0t=733.0rad/s10.0s=73.3rad/s2;
b. Using Equation 10.13, we have
ω2=ω02+2αΔθΔθ=ω2ω022α=0(733.0rad/s)22(73.3rad/s2)=3665.2radω2=ω02+2αΔθΔθ=ω2ω022α=0(733.0rad/s)22(73.3rad/s2)=3665.2rad

10.3

The angular acceleration is α=(5.00)rad/s20.0s=0.25rad/s2α=(5.00)rad/s20.0s=0.25rad/s2. Therefore, the total angle that the boy passes through is
Δθ=ω2ω022α=(5.0)202(0.25)=50radΔθ=ω2ω022α=(5.0)202(0.25)=50rad.
Thus, we calculate
s=rθ=5.0m(50.0rad)=250.0ms=rθ=5.0m(50.0rad)=250.0m.

10.4

The initial rotational kinetic energy of the propeller is
K0=12Iω2=12(800.0kg-m2)(4.0×2πrad/s)2=2.53×105JK0=12Iω2=12(800.0kg-m2)(4.0×2πrad/s)2=2.53×105J.
At 5.0 s the new rotational kinetic energy of the propeller is
Kf=2.03×105JKf=2.03×105J.
and the new angular velocity is
ω=2(2.03×105J)800.0kg-m2=22.53rad/sω=2(2.03×105J)800.0kg-m2=22.53rad/s
which is 3.58 rev/s.

10.5

Iparallel-axis=Icenter of mass+md2=mR2+mR2=2mR2Iparallel-axis=Icenter of mass+md2=mR2+mR2=2mR2

10.6

The angle between the lever arm and the force vector is 80°;80°; therefore, r=100m(sin80°)=98.5mr=100m(sin80°)=98.5m.

The cross product τ=r×Fτ=r×F gives a negative or clockwise torque.

The torque is then τ=rF=−98.5m(5.0×105N)=−4.9×107N·mτ=rF=−98.5m(5.0×105N)=−4.9×107N·m.

10.7

a. The angular acceleration is α=20.0(2π)rad/s010.0s=12.56rad/s2α=20.0(2π)rad/s010.0s=12.56rad/s2. Solving for the torque, we have iτi=Iα=(30.0kg·m2)(12.56rad/s2)=376.80N·miτi=Iα=(30.0kg·m2)(12.56rad/s2)=376.80N·m; b. The angular acceleration is α=020.0(2π)rad/s20.0s=−6.28rad/s2α=020.0(2π)rad/s20.0s=−6.28rad/s2. Solving for the torque, we have iτi=Iα=(30.0kg-m2)(−6.28rad/s2)=−188.50N·miτi=Iα=(30.0kg-m2)(−6.28rad/s2)=−188.50N·m

10.8

3 MW

Conceptual Questions

1.

The second hand rotates clockwise, so by the right-hand rule, the angular velocity vector is into the wall.

3.

They have the same angular velocity. Points further out on the bat have greater tangential speeds.

5.

straight line, linear in time variable

7.

constant

9.

The centripetal acceleration vector is perpendicular to the velocity vector.

11.

a. both; b. nonzero centripetal acceleration; c. both

13.

The hollow sphere, since the mass is distributed further away from the rotation axis.

15.

a. It decreases. b. The arms could be approximated with rods and the discus with a disk. The torso is near the axis of rotation so it doesn’t contribute much to the moment of inertia.

17.

Because the moment of inertia varies as the square of the distance to the axis of rotation. The mass of the rod located at distances greater than L/2 would provide the larger contribution to make its moment of inertia greater than the point mass at L/2.

19.

magnitude of the force, length of the lever arm, and angle of the lever arm and force vector

21.

The moment of inertia of the wheels is reduced, so a smaller torque is needed to accelerate them.

23.

yes

25.

|r||r| can be equal to the lever arm but never less than the lever arm

27.

If the forces are along the axis of rotation, or if they have the same lever arm and are applied at a point on the rod.

Problems

29.

ω=2πrad45.0s=0.14rad/sω=2πrad45.0s=0.14rad/s

31.

a. θ=sr=3.0m1.5m=2.0radθ=sr=3.0m1.5m=2.0rad; b. ω=2.0rad1.0s=2.0rad/sω=2.0rad1.0s=2.0rad/s; c. v2r=(3.0m/s)21.5m=6.0m/s2.v2r=(3.0m/s)21.5m=6.0m/s2.

33.

The propeller takes only Δt=Δωα=0rad/s10.0(2π)rad/s−2.0rad/s2=31.4sΔt=Δωα=0rad/s10.0(2π)rad/s−2.0rad/s2=31.4s to come to rest, when the propeller is at 0 rad/s, it would start rotating in the opposite direction. This would be impossible due to the magnitude of forces involved in getting the propeller to stop and start rotating in the opposite direction.

35.

a. ω=25.0(2.0s)=50.0rad/sω=25.0(2.0s)=50.0rad/s; b. α=dωdt=25.0rad/s2α=dωdt=25.0rad/s2

37.

a. ω=54.8rad/sω=54.8rad/s;
b. t=11.0st=11.0s

39.

a. 0.87rad/s20.87rad/s2;
b. θ=12,600radθ=12,600rad

41.

a. ω=42.0rad/sω=42.0rad/s;
b. θ=220radθ=220rad; c. vt=42m/sat=4.0m/s2vt=42m/sat=4.0m/s2

43.

a. ω=7.0rad/sω=7.0rad/s;
b. θ=22.5radθ=22.5rad; c. at=0.1m/sat=0.1m/s

45.

α=28.6rad/s2α=28.6rad/s2.

47.

r=0.78mr=0.78m

49.

a. α=−0.314rad/s2α=−0.314rad/s2,
b. ac=197.4m/s2ac=197.4m/s2; c. a=ac2+at2=197.42+(−6.28)2=197.5m/s2a=ac2+at2=197.42+(−6.28)2=197.5m/s2
θ=tan−1−6.28197.4=−1.8°θ=tan−1−6.28197.4=−1.8° in the clockwise direction from the centripetal acceleration vector

51.

ma=40.0kg(5.1m/s2)=204.0Nma=40.0kg(5.1m/s2)=204.0N
The maximum friction force is μSN=0.6(40.0kg)(9.8m/s2)=235.2NμSN=0.6(40.0kg)(9.8m/s2)=235.2N so the child does not fall off yet.

53.

vt=rω=1.0(2.0t)m/sac=vt2r=(2.0t)21.0m=4.0t2m/s2at(t)=rα(t)=rdωdt=1.0m(2.0)=2.0m/s2.vt=rω=1.0(2.0t)m/sac=vt2r=(2.0t)21.0m=4.0t2m/s2at(t)=rα(t)=rdωdt=1.0m(2.0)=2.0m/s2.
Plotting both accelerations gives

Figure shows a linear acceleration in meters per second squared plotted as a function of time in seconds. Centripetal starts at the origin of the coordinate system and grows exponentially with time. Tangential is positive and remains constant with time


The tangential acceleration is constant, while the centripetal acceleration is time dependent, and increases with time to values much greater than the tangential acceleration after t = 1s. For times less than 0.7 s and approaching zero the centripetal acceleration is much less than the tangential acceleration.

55.

a. K=2.56×1029J;K=2.56×1029J;
b. K=2.68×1033JK=2.68×1033J

57.

K=434.0JK=434.0J

59.

a. vf=86.5m/svf=86.5m/s;
b. The rotational rate of the propeller stays the same at 20 rev/s.

61.

K=3.95×1042JK=3.95×1042J

63.

a. I=0.315kg·m2I=0.315kg·m2;
b. K=621.8JK=621.8J

65.

I=736mL2I=736mL2

67.

v=7.14m/s.v=7.14m/s.

69.

θ=10.2°θ=10.2°

71.

F=30NF=30N

73.

a. 0.85m(55.0N)=46.75N·m0.85m(55.0N)=46.75N·m; b. It does not matter at what height you push.

75.

m2=4.9N·m9.8(0.3m)=1.67kgm2=4.9N·m9.8(0.3m)=1.67kg

77.

τnet=−9.0N·m+3.46N·m+03.38N·m=−8.92N·mτnet=−9.0N·m+3.46N·m+03.38N·m=−8.92N·m

79.

τ=5.66N·mτ=5.66N·m

81.

τ=57.82N·mτ=57.82N·m

83.

r×F=4.0i^+2.0j^16.0k^N·mr×F=4.0i^+2.0j^16.0k^N·m

85.

a. τ=(0.280m)(180.0N)=50.4N·mτ=(0.280m)(180.0N)=50.4N·m; b. α=17.14rad/s2α=17.14rad/s2;
c. α=17.04rad/s2α=17.04rad/s2

87.

τ=8.0N·mτ=8.0N·m

89.

τ=−43.6N·mτ=−43.6N·m

91.

a. α=1.4×10−10rad/s2α=1.4×10−10rad/s2;
b. τ=1.36×1028N-mτ=1.36×1028N-m; c. F=2.1×1021NF=2.1×1021N

93.

a=3.6m/s2a=3.6m/s2

95.

a. a=rα=14.7m/s2a=rα=14.7m/s2; b. a=L2α=34ga=L2α=34g

97.

τ=Pω=2.0×106W2.1rad/s=9.5×105N·mτ=Pω=2.0×106W2.1rad/s=9.5×105N·m

99.

a. K=888.50JK=888.50J;
b. Δθ=294.6revΔθ=294.6rev

101.

a. I=114.6kg·m2I=114.6kg·m2;
b. P=104,700WP=104,700W

103.

v=Lω=3Lgv=Lω=3Lg

105.

a. a=5.0m/s2a=5.0m/s2; b. W=1.25N·mW=1.25N·m

Additional Problems

107.

Δt=10.0sΔt=10.0s

109.

a. 0.06rad/s20.06rad/s2; b. θ=105.0radθ=105.0rad

111.

s=405.26ms=405.26m

113.

a. I=0.363kg·m2I=0.363kg·m2;
b. I=2.34kg·m2I=2.34kg·m2

115.

ω=6.68J4.4kgm2=1.23rad/sω=6.68J4.4kgm2=1.23rad/s

117.

F=23.3NF=23.3N

119.

α=190.0N-m2.94kg-m2=64.4rad/s2α=190.0N-m2.94kg-m2=64.4rad/s2

Challenge Problems

121.

a. ω=2.0t1.5t2ω=2.0t1.5t2; b. θ=t20.5t3θ=t20.5t3; c. θ=−400.0radθ=−400.0rad; d. the vector is at −0.66(360°)=−237.6°−0.66(360°)=−237.6°

123.

I=25mR2I=25mR2

125.

a. ω=8.2rad/sω=8.2rad/s; b. ω=8.0rad/sω=8.0rad/s

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