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Algebra and Trigonometry based Physics Formula sheet

Shadow J.Q. Robinson1

1

Department of Physics, Millsaps College, Jackson, MS 39210 [email protected]

The presence of a formula does not guarantee its use! Students are always welcome to suggest changes additions deletions corrections etc.

I.

UNIT PREFIXES

Giga (G)- 1 billion or 109 Mega (M)- 1 million or 106 kilo (k)- 1 thousand or 103 centi (c) - 1 hundredth or 10-2 milli (m) - 1 thousandth or 10-3 micro (µ) - 1 millionth or 10-6 nano (n) - 1 billionth or 10-9

where v is speed of particle and r is radius of the circular arc traveled by the particle. Centripetal Force = mass x centripetal acceleration. Newton's Law of Gravitation F =G M1 M2 R2 (11)

where G = 6.67 x 10-11 N m2 / kg2 , the M's are the masses of the two bodies and R is the distance between their centers. For a constant force, work is given by W = F dcos (12)

II.

EQUATIONS FOR PHYSICS EXAM

Always x - x0 = vavg t For constant acceleration v = v0 + at 1 (x - x0 ) = v0 t + at2 2 2 v 2 = v0 + 2a(x - x0 ) v + v0 vavg = 2 Acceleration from free fall a = -g = -9.8 m s2 (6) (2) (3) (4) (5) (1)

where F is the constant force, d is the displacement and is the angle between the F and d vectors. Work Energy Principle Wnet = KE 1 where KE = Kinetic Energy = mv 2 2 Force from spring F = -kx (14) (13)

where x is the displacement from equilibrium and k is the spring constant. Potential energies for conservative forces P Egrav = mgy 1 P Espring = kx2 2 Work by a conservative force (15) (16)

III.

DYNAMICS

Newton's Second Law Fnet = ma Force of kinetic friction (7)

Wcons = -P E If only conservative forces, KE + P E = 0

(17)

(18)

Ff r = µk N where N is the normal force. Force of static friction Ff r µs N

(8) Momentum p = mv (9) Newton's second Law in terms of momentum F = p t (20) (19)

where N is the normal force. Centripetal acceleration, points inward (along radius of circle) v2 aR = r (10)

For elastic head on collisions v1 - v2 = -(v1f - v2f ) (21)

2 For constant angular acceleration = 0 + t 1 = 0 t + t2 2 2 2 = 0 + 2 + 0 avg = 2 Relation to linear motion l = r v = r atan = r acentripetal = r 2 Torque = F rsin = I Moment of Inertia

2 I = mi ri

Bernoulli Equation (22) (23) (24) (25) Period of spring (26) (27) (28) (29) T = 2 Period of Pendulum T = 2 (30) (31) Wave velocity v = f (32) Wave Intensity I= P 4r2 (47) (46) L g (45) m k (44) f= 1 T (43) 1 1 P1 + 1 v 2 + gh1 = P2 + 2 v 2 + gh2 2 2 Frequency and Period (42)

Rotational Kinetic energy KErot = Angular momentum L = I Newton's second law = Conditions for equilibrium

IV.

1 2 I 2

(33)

Sound Intensity = 10log I I0 (48)

(34)

where I0 = 10-12 W/m2 . Doppler Effect f =f v ± vobs v ± vsource (49)

L t

(35)

ELECTRIC FORCE AND FIELDS

F = 0 = 0 Density m = V Pressure P = F A

(36) (37)

Force between two point charges q1 and q2 Felectric = kq1 q2 r2 (50)

(38)

(39)

where direction is given by repulsion or attraction of the charges. I am fine if you use the approximation of k=9x109 N m2 /C 2 Electric field of a point charge q E= kq r2 (51)

Pressure at depth h in fluid P = gh Atmospheric Pressure Patm = 1.103x105 Pascal Equation of continuity A1 1 v1 = A2 2 v2 (41) (40)

Electric fields relation to Electric force E= F q (52)

Electric Potential at any point in space defined as electric potential energy per unit charge

3

Va =

P Ea q

(53)

V = V0 sin(t) I = I0 sin(t) Root mean square values

(64) (65)

P E = qV

(54)

Inside a uniform electric field, the change in potential is given by Vba = -Ed (55)

I0 Irms = 2 V0 Vrms = 2 Power in AC circuit P = Irms Vrms Adding resistors in series Ref f = R1 + R2 + R3 Adding resistors in parallel 1 Ref f = 1 1 1 + + R1 R2 R3

(66) (67)

where E is the electric field and d is the distance traveled in the uniform field. For a point charge V = Capacitance C = Q/V For Parallel Plates A d (57) kq r (56)

(68)

(69)

(70)

Kirchoff's rules 1. Current into a junction = current out of a junction. 2. Total change in potential around closed loop = 0. SI Units for magnetic field Tesla , also sometimes see Gauss where 104 Gauss = 1 Tesla Force on electric current in a magnetic field F = IlBsin Force on moving charge in a magnetic field, F = qvBsin Magnetic field from a long straight wire (72) (71)

C=

0

(58)

1 Where 0 is given by the relation k= 4 In the presence of a dielectric with a dielectric constant , the value of 0 is replaced by 0 Energy stored in a capacitor PE = Ohm's Law V = IR (60) 1 1Q 1 QV = CV 2 = 2 2 2 C

2

(59)

B=

µ0 I 2r B t

(73)

V is potential difference in Volts, I is current in Amps, and R is resistance in Ohms which is denoted by . For a material, R= L A (61)

Induced electro-motive force = -N Transformer equation VS NS = VP NP velocity of light = c (74)

where is the resistivity and L is the length of wire and A is the cross sectional area. Temperature dependence T = 0 (1 + (T - T0 )) Power P = IV = I 2 R = V 2 /R AC Current Law of Reflection: (63) (62)

(75)

c = f = 3x108 m/s

(76)

i = r

(77)

4 Snell's Law or Law of Refraction n1 sin1 = n2 sin2 For mirrors and thin lenses: Microscope 1 1 1 + = do di f Magnification m= focal length for mirror f = R/2 (81) = -di do (80) is approximately fNflo . e Special Relativity Relativistic factor 1 1 - v 2 /c2 (89) (79) M= N l - fe fe d0 (78) M = -f0 /fe (87) for eye focused at the near point Telescope

(88)

Interference: Light interference gives a maxima when the waves have a total difference of an integer number of wavelength. It is a minimum when the waves have a half-integer difference. Wavelength in medium: 0 n

t = t0

(90)

L= (82)

L0

(91)

n =

m = m0

(92)

where 0 is the wavelength in a vacuum. Double Slit: Path difference = d sin where d is the separation of the slits and theta is the angle to the screen position measured from between the slits. For constructive dsin = n For destructive dsin = (n + 1/2) (84) (83)

Where the quantities with subscript 0 are the values recorded in the rest frame of the object, and the one without is the value measured by an observer seeing the object move at speed v and c is the speed of light. deBroglie wavelength h p

=

(93)

where h is Planck's constant and p is momentum.

Single slit: Diffraction minima are located at d sin = n where n is an integer. Reflection on thin films, if the light in a lower index of refraction bounces off of a higher n material, a phase change of 1/2 occurs. If light in a higher n material bounces off a lower n material, no change occurs. Magnifying glass M = N/f (85)

V.

ALGEBRA AND TRIGONOMETRY

sin2 + cos2 = 1 sin2 = 2sincos Quadratic formula ax2 + bx + c = 0 is solved by x= -b ± b2 - 4ac 2a

(94) (95)

(96)

for relaxed eye, N=near point of the eye, for adults approx 25 cm. M = N/f + 1 (86)

(97)

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