formula sheet apsc112

8/9/2019 Formula Sheet APSC112

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Formula Sheets for APSC 112(May be detached)

s r = arc length of a circle of radius rswept out by angle ( in radians)d v

dt r

angular velocity or speed; (v= tangential speed for circular motion)

2

2

tad d

dt dt r

= angular acceleration with tangential acceleration ta

2 2

r

var

r radial (centripetal) acceleration towards the centre

2 2 2 2

2 2

, , constant ,

2 , 2 , constant ,

1 1, , constant ,

2 2

1 1, , constant ,

2 2

o o

o o o o

o o o o

o o

v v at t a

v v a x x a

x x v t at t t a

x v v t t a

Centre of mass coordinates: , , ,1 1

1 1 1n n

cm i i cm i i cm i i

i i 1

n

i

x m x y m y z m z

M M M

Moment of Inertia: 2 2

1

n

i i

i

I m r r dm

, Parallel Axis Theorem:2

h cmI I Mh

Simple Harmonic Motion:2

2

20o

d

dt

or or2 0o

22

20o

d xx

dt

(Note that o is angular frequency; not the same as the angular velocity,d

dt

)

Period of Simple Harmonic Motion:2

o

T

,

12 ,o f f

T

2 2

( ) cos( ), ( ) sin( ), ( ) cos( ) ( )o o o o o ox t A t v t A t a t A t x

t

o

g

(simple pendulum), o

Mgh

I (physical pendulum), o

k

m (spring)

2 2

2 2, sin , ,

d dr F rF rF r F I I F ma m

dt dt

x

x

F k (Hookes Law), (torsion spring)

Kinetic energy = 21 1

2 2cm cm

2I Mv (rotation & translation) or 2

1

2I for a fixed axis

2 2

spring

1 1, ,

2 2torsion gravU kx U U m gy

( , ) sin ; 2 / ; /y x t A kx t k v k f ; /v T (on a string)

1 2beatf f f ;D

S

v vf f

v v

Work done by force: ,W F d P F

v

or by torque: ,f

i

W d P

K

Net f iW K K , f f i iK U K U W nc

Kinetic friction: k kf N ; Static friction: 0 s sf N

Formula Sheet 1/4


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Coulombs Law: 1 2 1 2 9 22 2

1, 8.99 10 Nm /

4 4o o

Q Q Q QF k k

r r

2C

Electric field:

(acting on q)F

E q

;

For a point charge Qlocated at the origin:2 2

4 o

Q kQE r

r r r

Absolute potential at rfrom point charge Q:4 o

Q kV

r r

Q

1

4

i ii

i io i

Q QV V k

r r

i i

Potential energy of Q1and Q2separated by r12:1 2 1 2

12 124 o

Q Q Q QU k

r r

1

4

i j i j

i j i jo ij ij

Q Q Q QU k

r r

Potential energy of Qwhere potential is V: U QV f

f ii

V V V E d

, / , / , /x y zE V x E V y E V z

p =dipole moment = Qd, Q = charge magnitude, d = separation of +QandQ

p

is directed fromQto +Q, ,p E U p E

Electric currentdQ

I J Adt

or ,J dA

current density dJ nqv

1 (or ) , , , =LV V IR E J RA

Power 2 2 /P IV I R V R

Temperature dependence: 1 ( ) or R 1 ( )o o o oT T R T T

Kirchhoffs Loop Rule: The algebraic sum of the changes in potential encountered in acomplete traversal of a closed loop in any circuit must be zero.

Kirchhoffs Junction Rule: The sum of the currents entering any junction must be equal to thesum of the currents leaving that junction.

1

,n

eq j

j

R R

nresistances in series;1

1,

n

jeq j

1

R R nresistances in parallel.

F Q E v B

, F I B , dF I d B

mvR

QB radius of trajectory of Qmoving with v B

, period of motion

2 mT

QB

Formula Sheet 2/4


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Magnetic dipole moment: ( normal of A)NIA NIAn n

,B NIA B U B NIA B

Biot-Savart Law2

4

o I d rdBr

, or34

o I d rdBr

7 64 10 Tm/A 1.26 10 Tm/Ao

Magnetic Field due to a long, straight, current-carrying wire:2

oI

Br

B Magnetic flux = orB A B dA

, induced emf = B

d

dt

Elementary charge 191.60 10 ,e C g Electron mass 319.11 10em k

Free fall acceleration at the earths surface 29.8 m/sg

1 V = 1 J/C, 1 N/C = 1 V/m, 1 A = 1 C/s, 1 = 1 V/A, 1 T = 1 N/Am

lndx

x ax a

,

3/2 1/222 2 2 2

1dx x

ax a x a

2 22 2

lndx

x x ax a

,1

2 2

1tan

dx x

x a a a

3/2 2 22 2

1xdx

x ax a

,2 2

2 2

xdxx a

x a

For small 21

, sin tan , cos 1 1 ( in radians)2

sin sin cos cos sin , cos cos cos sin sin

sin( ) sin( ) 2sin cos2 2

ln( ) ln ln , ln / ln lnab a b a b a b

3

6

9

12

10 milli m

10 micro

10 nano n

10 pico p

Formula Sheet 3/4


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Formula Sheet 4/4

formula sheet apsc112

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