AP Physics Mechanics Equations to Memorize Flashcards

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1
Q

<p>Integral of a differential</p>

A

<p>∫ dx = x + C</p>

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2
Q

<p>Derivative chain rule</p>

A

<p>d/dx (u) = (du / dv)(dv / dx)</p>

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3
Q

<p>Derivative quotient rule</p>

A

<p>d/dx (u / v) = (1/v)(du/dx) – (u/v2)(dv/dx)</p>

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4
Q

<p>Spring force</p>

A

<p>Fsp = -ks</p>

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5
Q

<p>Rule for the angle of the cross product</p>

A

<p>Rotate counterclockwise from the first vector to the second vector</p>

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6
Q

<p>Conservation of angular momentum</p>

A

<p>I1ω1 = I2ω2</p>

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7
Q

<p>Centripetal acceleration based upon ω</p>

A

<p>ac = ω2R</p>

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8
Q

<p>Relationship between the force and the change in energy per unit distance.</p>

A

<p>F = -dU/ds</p>

<p></p>

<p><span>This is a combination W = f x d and W = -ΔU</span></p>

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9
Q

<p>Rotational inertia of point masses</p>

A

<p>I = Σ(mr2)</p>

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10
Q

<p>Torque (2)</p>

A

<p>τ = F∙ r<span></span></p>

<p></p>

<p>( torque = force times "lever arm" )</p>

<p><span>(The lever arm is just the shortest distance between the axis of rotation and the path the force is acting along.)</span></p>

<p></p>

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11
Q

<p>Cartesian to polar coordinates (2)</p>

A

<p>v = √(vx2 + vy2)</p>

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12
Q

<p>Rotational work</p>

A

<p>Wrot­ = (τ)(Δθ)</p>

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13
Q

<p>Integral of an exponential term</p>

A

<p>∫ (eu)dx = (1/u’)(eu) + C</p>

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14
Q

<p>Slope of a velocity/time graph</p>

A

<p>Acceleration</p>

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15
Q

<p>Period of a simple pendulum</p>

A

<p>T = 2π√(L/g)</p>

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16
Q

<p>Centripetal force</p>

A

<p>Fc = mac</p>

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17
Q

<p>Integrating with a constant</p>

A

<p>∫ k f(x)dx = k ∫ f(x)dx</p>

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18
Q

<p>Kinetic friction</p>

A

<p>Fkf = ± μkf∙ FN</p>

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19
Q

<p>Period of a physical pendulum</p>

A

<p>T = 2π√(I/mgd)</p>

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20
Q

<p>Gravitational potential energy on a planet</p>

A

<p>Ug = mgh</p>

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21
Q

<p>Acceleration due to gravity</p>

A

<p>g = G∙mp/rp2</p>

<p></p>

<p><span>(This is pretty much just the Law of Universal Gravitation with the mass of the planet and the radius of the planet plugged in.)</span></p>

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22
Q

<p>Gravitational potential energy in space</p>

A

<p>Ug = (-G∙m1∙m2)/ r</p>

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23
Q

<p>Universal force of gravity</p>

A

<p>Fg = (G∙m1∙m2)/ r2</p>

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24
Q

<p>Acceleration</p>

A

<p>a = dv / dt</p>

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25
Q

<p>Slope of a potential energy / position graph</p>

A

<p>Negative of force</p>

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26
Q

<p>Displacement under constant acceleration</p>

A

<p>Δs = (vi)(Δt) + ½(a)(Δt2)</p>

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27
Q

<p>Power input by a force</p>

A

<p>P = W / Δt</p>

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28
Q

<p>Force down an incline</p>

A

<p>F<em>ll</em> = Fg ∙ sinθ</p>

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29
Q

<p>Area under an acceleration/time function</p>

A

<p>Change in velocity</p>

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30
Q

<p>Sum rule for integration</p>

A

<p>∫ (u + v)dx = ∫ (u)dx + ∫ (v)dx + C</p>

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31
Q

<p>Derivative of sin</p>

A

<p>d/dx (sin x) = cos x</p>

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32
Q

<p>Area under a force/position function</p>

A

<p>Work</p>

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33
Q

<p>Escape velocity</p>

A

<p>v = √2Gm / R</p>

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34
Q

<p>Constant acceleration</p>

A

<p>a = Δv / Δt</p>

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35
Q

<p>Derivative of cos</p>

A

<p>d/dx (cos x) = - sin x</p>

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36
Q

<p>Kinetic energy</p>

A

<p>K = ½ mv2</p>

37
Q

<p>vf2 equation</p>

A

<p>vf2 = vi2 + 2(a)(Δs)</p>

38
Q

<p>Potential energy in a spring</p>

A

<p>Usp= ½ ks2</p>

39
Q

<p>Displacement</p>

A

<p>Δs = sf – si</p>

40
Q

<p>Integral of sin</p>

A

<p>∫ (sin x)dx = -cos x + C</p>

41
Q

<p>Horizontal vector component</p>

A

<p>vx = v(cos θ)</p>

42
Q

<p>Formula for finding initial vertical velocity of a projectile given its initial velocity and angle at which it is fired.</p>

A

<p>vy = v(sin θ)</p>

43
Q

<p>Force in a gravitational field</p>

A

<p>Fg = -mg</p>

44
Q

<p>Power rule for integration</p>

A

<p>∫ f(xn)dx = (xn+1/n+1) + C</p>

45
Q

<p>Conservation of angular momentum</p>

A

<p>ΔL=0</p>

<p>if and only if</p>

<p>Στext = 0</p>

46
Q

<p>Rule for the angle of the dot product</p>

A

<p>Rotate counterclockwise from the first vector to the second vector</p>

47
Q

<p>Work done by a variable force</p>

A

<p>W = ∫(F)(ds)</p>

48
Q

<p>Newton’s second law for rotation</p>

A

<p>Στ = I∙α</p>

<p></p>

<p>(α is alpha, or angular acceleration )</p>

49
Q

<p>Work – potential energy relationship</p>

A

<p>-W = ΔU</p>

50
Q

<p>Momentum</p>

A

<p>p = mv</p>

51
Q

<p>Center of mass</p>

A

<p>rcm = (m1)(r1) + (m2)(r2) … / Σm</p>

52
Q

<p>Rotational kinetic energy</p>

A

<p>Krot = ½∙I∙ω2</p>

53
Q

<p>Relative motion</p>

A

<p>va,c = va,b + vb,c</p>

54
Q

<p>Integrating 1/x</p>

A

<p>∫ (1/x)dx = ln|x| + C</p>

55
Q

<p>Angular momentum (2)</p>

A

<p>L = rmv</p>

<p><span>also</span></p>

<p>L = Iω</p>

56
Q

<p>Impulse equation</p>

A

<p>J = Δp</p>

<p></p>

<p><span>( Impulse = change in momentum )</span></p>

57
Q

<p>Satellite velocity</p>

A

<p>vsat = √(G∙mcenteral / rorbit)</p>

58
Q

<p>Instantaneous power</p>

A

<p>P = F∙v</p>

59
Q

<p>Slope of a momentum/time graph</p>

A

<p>Force</p>

<p></p>

60
Q

<p>Derivative sum rule</p>

A

<p>d/dx (u + v) = du/dx + dv/dx</p>

61
Q

<p>Relationship between period and frequency</p>

A

<p>T = 1/f</p>

62
Q

<p>Area under a force/time function</p>

A

<p>Impulse</p>

63
Q

<p>Static friction</p>

A

<p>Fsf ≤ ± μsf ∙ FN</p>

64
Q

<p>Integral of cos</p>

A

<p>∫ (cos x)dx = sin x + C</p>

65
Q

<p>Work (2)</p>

A

<p>W = (F<em>ll</em>)(Δs)</p>

66
Q

<p>Impulse for a constant force</p>

A

<p>J = (ΣF)(Δt)</p>

<p></p>

<p><span>(Impulse = force x time)</span></p>

67
Q

<p>Work – energy theorem</p>

A

<p>ΣW = ΔK</p>

<p></p>

<p><span>( make sure you remember this one )</span></p>

68
Q

<p>Velocity</p>

A

<p>v = ds / dt</p>

69
Q

<p>Newton’s third law</p>

A

<p>Fab = -Fba</p>

70
Q

<p>Gravitational field lines</p>

A

<p>Vectors point how a test mass would accelerate</p>

71
Q

<p>Parallel axis theorem</p>

A

<p>I = Icm + md2</p>

<p></p>

<p>( If you know the moment of interia of an object rotating around its center of mass Icmbut the object is instead rotating around an axis that is distance "d" from the center of mass, the new rotational intertia can be found with this equation )</p>

72
Q

<p>Average velocity</p>

A

<p>vavg = Δs / Δt</p>

73
Q

<p>Area under a velocity/time function</p>

A

<p>Change in position</p>

74
Q

<p>Conservation of energy</p>

A

<p>ΣU + ΣK + ΣEth = constant for a closed system</p>

<p></p>

<p><span>( this is a simplification, as it does not include chemical potential energy, electrical potential energy, etc. )</span></p>

75
Q

<p>Period of a spring oscillator</p>

A

<p>T = 2π√(m/k)</p>

76
Q

<p>Centripetal acceleration based upon v</p>

A

<p>ac = v2 / r</p>

77
Q

<p>Speed</p>

A

<p>S = distance / time</p>

78
Q

<p>Impulse for a variable force</p>

A

<p>J = ∫(F)(dt)</p>

79
Q

<p>Newton’s second law</p>

A

<p>ΣF = ma</p>

<p><span>(don't forget how many times you could get 1 point on a free response simply by writing this down)</span></p>

80
Q

<p>Angular frequency (2)</p>

A

<p>ω = 2πf</p>

81
Q

<p>Slope of a position/time graph</p>

A

<p>Velocity</p>

82
Q

<p>Average velocity when acceleration is constant</p>

A

<p>vavg = (vi + vf ) / 2</p>

83
Q

<p>Force perpendicular to an incline</p>

A

<p>FN = Fg ∙ cosθ</p>

84
Q

<p>Conservation of momentum</p>

A

<p>Σpi = Σpf if ΣFext = 0</p>

<p></p>

<p><span>( With no external forces, the momentum of a system will be conserved )</span></p>

<p><span>( This is true for both linear and angular momentum )</span></p>

85
Q

<p>Power (general)</p>

A

<p>P = ΔE / Δt</p>

86
Q

<p>Rotational instantaneous power</p>

A

<p>P = τ·ω</p>

87
Q

<p>Derivative product rule</p>

A

<p>d/dx (uv) = v(du/dx) + u(dv/dx)</p>

88
Q

<p>Rotational inertia of radially symmetric objects</p>

A

<p>I = kMR2</p>

<p></p>

<p>( k = the number of these objects )</p>

89
Q

<p>Equations for rolling (3)</p>

A

<p>ds = r∙dθ</p>