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AP Physics Chapter 2-4 Key Equations and Ideas Vectors a b (ax bx )î (ay by )ĵ (az bz )k̂ a b ab cos ax bx a y by az bz (dot product) a x b ab sin ĵ î k̂ î ĵ k̂ a y az ax a y ax az a x b ax a y az î ĵ k̂ ( a y bz az by ) î ( ax bz az bx ) ĵ ( ax by a y bx ) k̂ by bz bx bz bx by bx by bz Direction of a x b (vector product) is determined by the right-hand rule î x ĵ k̂ ĵ x k̂ î k̂ x î ĵ ĵ x î k̂ k̂ x ĵ î î x k̂ ĵ y 2-D x = r cos y = r sin 1-D Acceleration y = tan-1 x x x x2 – x1 r2 - r1 x v dt area under vt graph dy dr dx dz î ĵ k̂ dt dt dt dt v a dt slope on xt graph area under at graph x t dx vinst dt v a avg t dv ainst dt v avg Velocity x2 y 2 3-D r x î yĵ zk̂ Position Displacement r r Comments r dvy dv dv dvx î ĵ z k̂ dt dt dt dt x2 y 2 z2 slope on vt graph Projectiles Kinematic Equations x = vx0t = (v0cos 0)t (constant accel) y = vy0t – ½gt2 = (v0sin 0)t - ½gt2 2 xf = xi + vit + ½at vf = vi + at For symmetric projectiles v TMaxHeight o sin o g vf2 = vi2 + 2a(xf – xi) xf = xi + ½(vf + vi)t Uniform Circular Motion v2 r d 2r T= v v ac Fc mac m r ac v v2 r v2 R xMax o sin 2 o g TTotal 2vo sin o g v 2yo H yMax 2g (vo sin o )2 2g Key Ideas: Use dimensional analysis (also called the factor-label method or chain-link conversions) to convert from one unit to another. This is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in desired set of dimensional units is obtained. Use significant figures in your calculations. Keep a couple of extra significant figures in the interim steps. Do not round until the final answer. The order of magnitude is the power of ten when the number is expressed in scientific notation. Carry the units in each problem. This will serve as a check when you get to the final answer. Always use (or convert to) SI units. If the signs of the velocity and acceleration of an object are the same, the speed will increase. If the signs are opposite, the speed decreases. Is your answer sensible? Think about the reasonableness of your answer. If the angle between two vectors is 0o, the dot product is a maximum. If the angle is 90o, the dot product is zero. If the angle between two vectors is 0o, the vector (cross) product is zero. If the angle is 90o, the vector product is a maximum. When determining the angle between two vectors, they must be arranged tail-to-tail. To determine the direction of the resultant vector of a vector product, use the right-hand rule and sweep the first vector into the second vector. Your thumb will determine the direction of the resultant vector. The direction of the instantaneous velocity of an object is always tangent to the path of the object’s position. In projectile motion, the horizontal motion and the vertical motion are independent of one another. Neither motion affects the other. Solve a problem as far as you can algebraically (i.e. with letters and symbols). Substitute in numbers in the final step.