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AP Physics formula list (B1) Ch. 2 Motion in one Dimension Displacement: x x f xi Average velocity (all situations): v d t v Average velocity (uniform acceleration): a Average acceleration: v f vi v vi v f v t d 2 1 (v f vi )t 2 2 Kinematic formulas: v f vi at d vi t ½at 2 v f vi 2ad 2 2 Kinematic formulas if vi=0: v f 2ad 2d a t a 2d t2 Ch. 3 Motion in two Dimensions x-component y-component vix vi cos viy vi sin v fx vix a x t v fy viy a y t d x vixt ½ a x t 2 d y viyt ½a y t 2 v fx vix 2a x d x v fy viy 2a y d y ax 0 a y 9.8m / s 2 (IF UP IS POSITIVE) 2 2 2 2 (B1) Ch. 4 Laws of Motion Net force: F ma Friction equations: Weight: W Fg mg Static: F f s Fn x and y components (if θ is to horizontal axis): Net force using x and y components: Atwood Machine: a Fnet ( M m) g M m Kinetic: F f Fx F cos Fy F sin F F 2 x k Fn 2 y (B1) Ch. 5 Work and Energy Work: W F d F d cos Net work: Wnet KE Total Energy: Work done against friction: W f F f d Work done against gravity: Wg PE mgh ET PE KE Q Total mechanical energy: MEt KEi PEi KE f PE f = constant KE ½mv 2 Kinetic energy: Gravitational PE: PE mgh Elastic PE: PEs ½kx 2 P Power Equations: W Fd mgh Fv t t t (B1) Ch. 6 Momentum and Collisions Impulse (IS A VECTOR: you will need signs if vf and vi are different directions, or J is opposite direction of motion): J p Ft mv p mv Momentum: Conservation of momentum (IS A VECTOR: you will need signs if vf and vi are opposite directions): m1v1i m2 v2i m1v1 f m2 v2 f m1 m2 vi m1v1 f Explosion: m2 v 2 f p p Elastic Collision: i f AND: KE KE i The perfectly elastic equation (use with conservation of momentum: p p Inelastic Collision: i f KE KE i f f v1i v2i (v1 f v2 f ) Q Perfect Inelastic: m1v1i m2 v2i m1 m2 v f (NOTE: This equation is also used to find the v of the center of mass (com). v f is vcom!) Glancing collisions: p ix p fx AND: p iy p fy Note: px p cos p y p sin (if θ is to the horizontal!) Center of mass: xcm m x m i i i (chose a common origin for all point masses so all positions (all xi and xcm) are relative to that origin.) (B1) Ch. 7&8 Circular Motion & Torque Linear velocity for an object moving in a circle: v 2r T v2 Centripetal (radial) acceleration: a c r mv 2 r Gm1 m2 Gravitational force between two masses: Fg r2 Orbital motion: Frad Fc Fg Centripetal force: Frad Fc mac r 3 Gmcentral Kepler’s Third Law (Good derivation practice from above 3 equations): T2 4 2 Pendulum motion/rollercoaster motion: Frad Fc Fn Fg FT Fg Acceleration due to gravity: gp (If not at top or bottom of circle, you might have to find components of Fg (if FT is toward center) or find components of FT (If FT is NOT toward center)) Gm p r2 Gravitational potential energy between two masses: U g Gm1m2 r (This can be used in conservation of energy equation just like mgh) Escape velocity (a good practice in derivation from conservation of energy using the above equation and ½ mv 2: Torque: F d Fd sin θ= angle between force and lever arm Equilibrium: F x net 0 0 F y 0 cw ccw v 2Gmp r Angular Quantities Note: Remember all kinematic angular quantities ( , , ) are multiplied by r to get the linear quantity (d,v,a). All Newtonian Angular quantities ( ,, L ) are divided by r (or r in the case of I) to get the linear quantity (F, m, mv). 2 Angular displacement (1 rev): s 2r 2 r r Angular velocity: 2 t t1rev Angular to linear velocity conversion: v r Angular acceleration: t Angular to linear acceleration conversion: at r Angular Mass (?) (a.k.a MOMENT OF INERTIA): Angular Force: Angular momentum: I L I mvr (for orbiting point masses) Conservation of Angular Momentum: Angular Impulse(?): I mr 2 (β=1 for orbiting point masses) L L L t Rotational Kinetic Energy: K rot 1 2 I 2 i f I ii I f f mvi ri mv f rf (B2) Ch. 9&10 Fluid Mechanics Density: m v F A F1 F2 A1 A2 Pressure: P Hydraulic (Pascal’s) Principle: Gauge pressure: Pgauge P gh Absolute pressure: Pabs Pgauge Patm Buoyant force: FB m fluid g fluidV fluid g If floating: F 0 F B Fg (object) (use V of water displaced!) If sinking or completely submerged: Continuity equation: F ma F Flow rate B Fg (object) (use V of object!) V A1v2 A2 v2 t Bernoulli’s equation: P1 ½ v1 gh1 P2 ½ v2 gh2 2 2 (If P1 is higher than P2, and P1=Patm, then P2=Pabs. BUT, If P1 is set to zero, P2=Pgauge) Torricelli’s equation (STATE IT): v 2 gh Note: There could be a third force such as tension or spring force. (B2) Ch. 12&13 Thermodynamics L Lo T Linear expansion: H Rate of heat transfer by conduction: Q kA t L W PV Work done ON a gas: Internal Energy Equations: U Q W (ΔU=0 for a cycle of a cyclical process since ΔT=0) 3 3 K avg U k B T nRT 2 2 Root mean square velocity: vrms Ideal gas equation: 3k BT PV nRT NkBT 3RT M Heat engine: Efficiency equations (%efficiency = e x 100): Carnot Efficiency: e e Wout Pout QH Pin Wout QH QC TH TC TH (B1) Ch. 14&15 Simple Harmonic Motion (SHM), Vibrations and Waves Hooke’s Law: Fs kx 2 t ) A cos( 2ft ) T 2 t )) A ( sin( 2ft )) Velocity MAX: vmax A Velocity of a system in SHM: v A ( sin( t )) A ( sin( T Displacement of a system in SHM: x A cos(t ) A cos( Acceleration of a system in SHM: a A 2 ( cos(t )) A 2 ( cos( Period of mass/spring system: 2 Wave velocity equations: v f v Wave velocity in a vibrating string: v F Doppler effect: f ' f V Vo V Vs m L m k 2 t )) A 2 ( cos( 2ft )) Thus: amax A 2 T Period of pendulum: 2 L g Frequency of standing waves on a string: (at fo, λ=2L) fn nv n 2L 2L FT n = 1,2,3,4… Frequency of standing waves in air column open: (at fo, λ=2L) fn nv 2L n = 1,2,3,4… Frequency of standing waves in air column with 1 closed end: (at fo, λ=4L) fn nv 4L n = 1,3,5,7… Consecutive resonances in a variable length air column with 1 closed end vibrating at frequency f: L2 L1 (B2) Ch. 23 & 24 Light Index of refraction: n c v n1 sin 1 n2 sin 2 n Critical angle: sin c int o n from Snell’s Law: (B2) Ch. 26 Diffraction and Thin Films Double Slit path difference: d sin m Constructive (mth maxima): m = 1,2,3,4… Destructive (mth minima): m = ½, 3/2, 5/2, 7/2… Equating θ to X and L: tan X L Approximation: d X L Single Slit Path difference (DESTRUCTIVE, ONLY): (mth minima): d sin m m = 1,2,3,4… 2 Thin Film: 2-phase shift Constructive: 2t= λ or: t m film 2 m0 m=1,2,3… 2n Destructive: 2t= λ/2 or: t m film 4 m0 4n m=1,3,5… m0 4n m=1,3,5… Soap Bubble: 1-phase shift: Constructive: 2t= λ/2 or: t m film 4 Destructive: 2t= λ or: t m film 2 m0 2n m=1,2,3… (B2) Ch. 25 Mirrors and Lenses Magnification: M hi d i ho do Object/image distance equation: Lensmakers’ equation: to see that: 1 1 1 (n 1) f R1 R2 1 1 1 do di f n 1 f (B1 and B2) Ch. 16&17 Electricity Force on a point charge: FE qE E F q W qV Work done on a point charge: Get this RIGHT! or: V, U, (include sign of charge) E and F (ignore sign) for POINT CHARGE(S): kq1q 2 r kq q F 12 2 r kq r kq E 2 r V U elec k 1 40 V, E, Q and C for PARALLEL PLATES: V Ed Voltage between the plates: Capacitance equations (If hooked up to a battery: V is constant. If battery is disconnected and capacitor isolated after charging: Q is constant): C Q k o A or Q VC V d Energy stored in a capacitor: E ½CV 2 ½QV 1 1 1 1 ... CT C1 C 2 C3 VT V1 V2 V3 ... QT Q1 Q2 Q3 ... Capacitors in series: Capacitors in parallel: CT C1 C2 C3 ... VT V1 V2 V3 ... QT Q1 Q2 Q3 ... (B1 and B2) Ch. 18&19 Resistors and Circuits Current: I q t Resistance: R L Ohms’ Law: A V2 W Power equations: P IV I 2 R R t Vterm I T r Terminal voltage of a battery: Resistors in series: RT R1 R2 R3 ... VT V1 V2 V3 ... I T I1 I 2 I 3 ... PT P1 P2 P3 ... Resistors in parallel: 1 1 1 1 ... RT R1 R2 R3 VT V1 V2 V3 ... I T I1 I 2 I 3 ... PT P1 P2 P3 ... V IR (B2) Ch. 20&21 Magnetism Force on a moving charge in an external B: FB qv B qvBsin mv qB FB IL B BIL sin FB FC or: r For charge moving in a circular path in external B: Force on a current-carrying wire in an external B: B Strength of B due to a wire: Flux equation: o I 4x10 7 I 2r 2r BA cos induced Induced EMF in a coil: n I induced R t Motional EMF on a straight wire: induced BLv I induced R Modern Physics Energy of a photon: E photon hf Photoelectric Effect: hc KEmax Ei hf i hf c hc Work function: hf c KEmax equation: KEmax qVs (q=1e) X-ray emission: qV hf max (q=1e) Compton Effect: Eincident KEe Escattered Debroglie Wavelength: Bohr Model: c p mv m m r p or: m 1u=931MeV 1 T1 N N0 2 2 h mv hc E mc 2 t Half Life: E Ei E f hf Equivalence of mass and energy: Mass defect: h c f