PY 205 Sample Equation sheet Fall 2023 Things you must know Definition of average velocity Definition of momentum Definition of particle energy The Energy Principle Definition of kinetic energy Definition of work The Momentum Principle Other fundamental principles LA net A t d LA dt net A A rA F Ltrans A rA p point particle Multiparticle systems rcm m1 r1 m2 r2 m1 m2 Krel Krot Kvib Ltrans A rcm A Ptot ptot Mtot vcm v c Ktrans 1 2 Lrot I Mtot vcm 2 v c I m1r2 1 m2r2 2 Ktot Ktrans Krel L2 rot 2I I 2 Krot LA Ltrans A Lrot 1 2 R R 1 2 Sphere 2 5 I Cylinder Disc M R2 I M R2 R Thin Hoop I M R2 R L Rod Cylinder Disc I I 1 4 1 M L2 M R2 12 M L2 for R L 1 12 t 1 2 F net m t 2 cid 16 cid 17 a d v dt Other physical relationships cid 18 Fnet x cid 19 t2 m m p i r f r i E2 pc 2 cid 0 mc2 cid 1 2 cid 12 cid 12 cid 12 cid 12 cid 18 d p cid 12 cid 12 cid 12 cid 12 cid 19 m v 2 cid 12 cid 12 cid 12 mg near Earth cid 12 cid 12 cid 12 Fgrav cid 12 cid 12 cid 12 L cid 12 cid 12 cid 12 L0 Uspring p v R kss2 dt R 1 2 static Ffriction sFN Felec Ugrav mg y near Earth Uelec x t xi vixt 1 2 1 cid 115 cid 18 v 1 cid 19 2 c m1m2 r 2 r m1m2 r Fgrav G Ugrav G Fspring kss L s sliding Ffriction kFN Y F A L L macro Y micro speed of sound v d ksi d 1 1 4 0 4 0 q1q2 r 2 r q1q2 r 2 C A v 2 cid 114 ks cid 12 cid 12 cid 12 1 m cid 12 cid 12 cid 12 Fair with and f 1 T 2 T cid 114 ksi ma if v c where R radius of kissing circle 1 ksis2 EM interatomic pot energy Ui 1 2 EN 13 6eV EN N 0 E0 where N 0 1 2 and 0 N 2 where N 1 2 3 Hydrogen atom energy levels cid 114 ksi ma Quantized oscillator energy levels q N 1 q N 1 q N 1Cq Ethermal mC T S k ln C atom E T S E 1 T prob E E e E kBT Symbol Approximate Value Constant Speed of light Gravitational constant Approx grav field near Earth s surface Electron mass Proton mass Neutron mass Electric constant Proton charge Electron volt Avogadro s number Plank s constant hbar h 2 specific heat capacity of water Boltzmann constant Room temperature c G g me mp mn 1 4 0 e 1 eV NA h C kB Troom K 1 103 milli m 1 10 3 1 10 6 mega M 1 106 micro G 1 109 1 10 9 n nano 1 10 12 T 1 1012 pico p giga tera kilo 3 108 m s 6 7 10 11 N m2 kg2 9 8 N kg 9 1 10 31 kg 1 67 10 27 kg 1 67 10 27 kg 9 109 N m2 C2 1 6 10 19 C 1 6 10 19 J 6 02 1023 atoms mol 6 6 10 34 J s 1 05 10 34 J s 4 2 kJ kg C 1 38 10 23 J K 293 15 K f cos x cos y cos z unit vector from angles A B AxBx AyBy AzBz A B AyBz AzBy AzBx AxBz AxBy AyBx cid 12 cid 12 cid 12 cos cid 12 cid 12 cid 12 cid 12 cid 12 cid 12 B cid 12 cid 12 cid 12 A cid 12 cid 12 cid 12 A B cid 12 cid 12 cid 12 cid 12 cid 12 cid 12 A cid 12 cid 12 cid 12 cid 12 cid 12 cid 12 B cid 12 cid 12 cid 12 sin 2