AP Physics Mechanics Equations to Memorize Flashcards
<p>Integral of a differential</p>
<p>∫ dx = x + C</p>
<p>Derivative chain rule</p>
<p>d/dx (u) = (du / dv)(dv / dx)</p>
<p>Derivative quotient rule</p>
<p>d/dx (u / v) = (1/v)(du/dx) – (u/v2)(dv/dx)</p>
<p>Spring force</p>
<p>Fsp = -ks</p>
<p>Rule for the angle of the cross product</p>
<p>Rotate counterclockwise from the first vector to the second vector</p>
<p>Conservation of angular momentum</p>
<p>I1ω1 = I2ω2</p>
<p>Centripetal acceleration based upon ω</p>
<p>ac = ω2R</p>
<p>Relationship between the force and the change in energy per unit distance.</p>
<p>F = -dU/ds</p>
<p></p>
<p><span>This is a combination W = f x d and W = -ΔU</span></p>
<p>Rotational inertia of point masses</p>
<p>I = Σ(mr2)</p>
<p>Torque (2)</p>
<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>
<p>Cartesian to polar coordinates (2)</p>
<p>v = √(vx2 + vy2)</p>
<p>Rotational work</p>
<p>Wrot = (τ)(Δθ)</p>
<p>Integral of an exponential term</p>
<p>∫ (eu)dx = (1/u’)(eu) + C</p>
<p>Slope of a velocity/time graph</p>
<p>Acceleration</p>
<p>Period of a simple pendulum</p>
<p>T = 2π√(L/g)</p>
<p>Centripetal force</p>
<p>Fc = mac</p>
<p>Integrating with a constant</p>
<p>∫ k f(x)dx = k ∫ f(x)dx</p>
<p>Kinetic friction</p>
<p>Fkf = ± μkf∙ FN</p>
<p>Period of a physical pendulum</p>
<p>T = 2π√(I/mgd)</p>
<p>Gravitational potential energy on a planet</p>
<p>Ug = mgh</p>
<p>Acceleration due to gravity</p>
<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>
<p>Gravitational potential energy in space</p>
<p>Ug = (-G∙m1∙m2)/ r</p>
<p>Universal force of gravity</p>
<p>Fg = (G∙m1∙m2)/ r2</p>
<p>Acceleration</p>
<p>a = dv / dt</p>
<p>Slope of a potential energy / position graph</p>
<p>Negative of force</p>
<p>Displacement under constant acceleration</p>
<p>Δs = (vi)(Δt) + ½(a)(Δt2)</p>
<p>Power input by a force</p>
<p>P = W / Δt</p>
<p>Force down an incline</p>
<p>F<em>ll</em> = Fg ∙ sinθ</p>
<p>Area under an acceleration/time function</p>
<p>Change in velocity</p>
<p>Sum rule for integration</p>
<p>∫ (u + v)dx = ∫ (u)dx + ∫ (v)dx + C</p>
<p>Derivative of sin</p>
<p>d/dx (sin x) = cos x</p>
<p>Area under a force/position function</p>
<p>Work</p>
<p>Escape velocity</p>
<p>v = √2Gm / R</p>
<p>Constant acceleration</p>
<p>a = Δv / Δt</p>
<p>Derivative of cos</p>
<p>d/dx (cos x) = - sin x</p>