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Velocity - v=Δd/Δt (m/s) Acceleration - a=Δv/Δt (m/s²) Force - F=ma (N) Newton - kg x m/s² Work - Fd (J) KE - ½mv² (J) PE (gravitational) - mgh (J) Power (as related to work) - W/∆t=fv (J/s) J/s - kg x m² / s² Density - ρ=m/V(volume) (kg/m²) Pressure - P=F/A (A=πr² for a circle) (Pascals) Hydrostatic Pressure (measured at a depth d from the surface of a liquid) - pogd (Pascal) P=measured pressure, g=gravity, d=depth from surface Pascal - kg/ms² SI Unit of Length - m (meter) SI Unit of Mass - kg (kilogram) SI Unit of Time - s (second)
SI Unit of Electric Current - A (amperes) SI Unit of Temperature - K (kelvin) SI Unit of Luminous Intensity - Cd (candela) Derived Unit of Volume - m³ Derived Unit of Force - N (Newton) Derived Unit of Energy/Work - J (Joule) Derived Unit of Power - W (Watt) Derived Unit of Pressure - Pa (Pascal) Derived Unit of Charge - C (Coulomb) Derived Unit of Resistance - Ω (Ohms) Derived Unit of Capacitance - F (Farads) Pythagorean Theorem - a² + b² = c² Vectors - Magnitude and direction Scalars - Magnitude only Sin 90° - 1 Sin 60° - 0. Sin 30° - 0. Sin 0° - 0 Cos 90° - 0
vf²= v0² + 2ad (constant a - no time given) Projectile Motion - Time to max ht: 0-v(yi)/g max ht: =v(yavg)t=v(yi)/2 x tup total time = 2t(up) Horizontal displacement: v(x)t(total) Newton's First Law - An object's velocity remains constant unless a net force is acting upon it (∑F=0, v=constant) Newton's Second Law - ∑F=ma Newton's Third Law - For every force exerted by one object on a second object, there is an equal but opposite force by the second object on the first F(2-1)=-F(1-2) Weight - W=mg (kg) Force of Gravity - F=G m₁m₂/r² (G=6.67x10⁻¹¹, on earth G=9.8m/s²) Kinetic Friction - Ff= μ(k)F(N) Static Friction - Ff= μ(s)mn(normal force) Centripetal Acceleration - ac= v²/r Centripetal Force - F= mv²/r=mac Total Mechanical Energy - E = KE+PE Conservation of ME - ½mv²(i) + mgh(i) = ½mv²(f) + mgh(f) (no work done by conservative forces)
W=∆E (work performed by nonconservative forces, ME is not conserved) Work Energy Theorem - W=∆KE Momentum - p=mv Impulse-Momentum Theorem - F∆t=∆mv COLLISIONS - SEE SHEET Angular Displacement - ∆θ (d= r) Angular Velocity - ω=∆θ/∆t (v=r ω) Angular Acceleration - α=∆ ω/∆t (a=rα) SEE ROTATIONAL KINEMATICS EQUATIONS - SEE ROTATIONAL KINEMATICS EQUATIONS Center of Mass - t=m₁x₁ +m₂x₂..../m₁+m₂.... Torque - =Fx(lever arm) or t=Iα Inertia - I=∑mr² (for pt masses about an axis) Angular Momentum - L=I ω Rotational KE - ½ I ω² Specific Gravity - p/p(water) p(h₂o) - 1000kg/m³ Archimedes Principle (Buoyancy Force) - W(fluid displaced)=p(fluid)V(submerged)g If floating, Fb=Wobject
Doppler Effect SEE SHEET - SAME THING 2X - Fo=Fs v±Vo/V±vs Fo>Fs object and source are moving towards each other Fs Elasticity of Solids - modulus x strain Young's Modulus Stretching/Compression - F/A = Y ∆L/L₀ Shear Deformation - F/A = S ∆X/L₀ Bulk Modulus Volume Deformation - AP = -B∆V/V₀ Coulomb's Law - F = k q₁q₂/r² Electric Field due to a point charge - E = k q/r² Resistors in Series - Req = R₁ + R₂ + ..... same current, diff voltage Resistors in Parallel - 1/Req = 1/R₁ + 1/R₂ + .... diff current, same voltage Power (as related to current/electricity) - P = VI = I²R = V²/R AC V(rms) - V(rms) = V(max)/√ AC I(rms) - I(rms) = I(max)/√ Parallel Plate Capacitor - C = (k)ε₀ A/d V=Ed PE in Capacitor - PE = ½CV²
Capacitors in Series - 1/Ceq = 1/C₁ + 1/C₂ + .... Capacitors in Parallel - Ceq = C₁ + C₂ + .... Charged Particle in Mag. Field - F = qvBsinθ RHR: thumb = v, fingers = B, palm = force Current-carrying wire in a Magnetic Field - F = ILBsinθ RHR: thumb = I, fingers = B, palm = force Magnetic Field due to a current carrying wire - B = μ₀I/2πr RHR: thumb = I, fingers (curled) = B XXXXXXXXXX - Into page (away from me) oooooooooo - Out of page (towards me) Light - λf = v Energy of a photon - E = hf = hc/λ Law of Reflection - Angle of Incidence = Angle of reflection Snell's Law of Refraction - n₁sinθ₁ = n₂sinθ₂ Index of refraction - n = c/v Total internal reflection - Sinθ = n₂/n₁ Double Slit Interference: Bright Fringes - dsinθ = mλ Double Slit Interference: Dark Fringes - dsinθ = (m+½)λ Diffraction Grating: Bright Fringes - dsinθ=mλ Single Slit Diffraction: Dark Fringes - asinθ=mλ
