# Projectile motion horizontal x x ? v ? t 0 vertical y

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Projectile Motion Horizontal: x-x ο = v ο •t + 0 Vertical: y-y ο = v ο •t + ½•a•t² #46 Centripetal Force r m r mv F 2 2 ω = = #47 Kirchhoff’s Laws Loop Rule: Σ Around any loop V i = 0 Node Rule: Σ at any node I i = 0 #51 Minimum Speed at the top of a Vertical Circular Loop rg v = #53 Resistor Combinations SERIES R eq = R 1 + R 2 + R 3 +. . . PARALLEL = = + + + = n i i n eq R R R R R 1 2 1 1 1 1 1 1 K #54 Newton's Second Law and Rotational Inertia τ = t orque = I• α I = moment of inertia = m•r² (for a point mass) (See table in Lesson 58 for I of 3D shapes.) #55 Circular Unbanked Tracks mg r mv µ = 2 #56 Continuity of Fluid Flow A in •v in = A out •v out A= Area v = velocity #58 Moment of Inertia - I cylindrical hoop m•r 2 solid cylinder or disk ½ m•r 2 solid sphere 2 / 5 m•r 2 hollow sphere m•r 2 thin rod (center) 1 / 12 m•L 2 thin rod (end) m•L 2 #59 Capacitors Q = C•V Q = charge on the capacitor C = capacitance of the capacitor V = voltage applied to the capacitor RC Circuits (Discharging) V c = V o •e t/RC V c I•R = 0 #60 Thermal Expansion Linear: L = L o α T Volume: V = V o β T #61 Bernoulli's Equation P + ρ •g•h + ½• ρ •v ² = constant Q Volume Flow Rate = A 1 •v 1 = A 2 •v 2 = constant #62 Rotational Kinetic Energy (See LEM, pg 8) KE rotational = ½•I• ω 2 = ½•I• (v / r) 2 KE rolling w/o slipping = ½•m•v 2 + ½•I• ω 2 Angular Momentum = L = I• ω = m•v•r•sin θ Angular Impulse equals CHANGE IN Angular Momentum L = τ orque t = (I• ω )

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Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 3 of 8 Version 5/12/2005 #63 Period of Simple Harmonic Motion k m T π 2 = where k = spring constant f = 1 / T = 1 / period #64 Banked Circular Tracks v 2 = r g tan θ #66 First Law of Thermodynamics U = Q Net + W Net Change in Internal Energy of a system = +Net Heat added to the system +Net Work done on the system Flow of Heat through a Solid Q / t = k•A• T / L k = thermal conductivity A = area of solid L = thickness of solid #68 Potential Energy stored in a Capacitor P = ½•C•V² RC Circuit formula (Charging) V c = V cell •(1 e t / RC ) R•C = τ = time constant V cell - V capacitor I•R = 0 #71 Simple Pendulum g L T π 2 = and f = 1/ T #72 Sinusoidal motion x = A•cos( ω •t) = A•cos( 2 π f •t) ω = angular frequency f = frequency #73 Doppler Effect s Toward Away o Toward Away v v f f m 343 343 ± = v o = velocity of observer : v s = velocity of source #74 2 nd Law of Thermodynamics The change in internal energy of a system is U = Q Added + W Done On – Q lost – W Done By Maximum Efficiency of a Heat Engine (Carnot Cycle) (Temperatures in Kelvin) #75 Thin Lens Equation f = focal length i = image distance o = object distance Magnification M = D i / D o = i / o = H i / H o Helpful reminders for mirrors and lenses Focal Length of: positive negative mirror concave convex lens converging diverging Object distance = o all objects Object height = H o all objects Image distance = i real virtual Image height = H i virtual, upright real, inverted Magnification virtual, upright real, inverted #76
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