K

ar

t

a

w zor

ó

w

i

s

t

ał yc

h

f

i zyczn yc

h

(

p rzy

j

ę

t

o

t

y p ow e

ozn aczen i a)

Kinematyka

v

a

t

∆

=

∆

;

0

( )

v t

v

at

=

±

;

2

0

( )

2

at

s t

v t

=

±

;

Dynamika

F

ma

=

;

p

mv

=

;

p

F

t

∆

=

∆

;

T

N

F

F

µ

=

;

)

,

(

cos

s

F

Fs

W

r

s

∠

=

;

2

2

kin

mv

E

=

;

W

P

t

∆

=

∆

;

Grawitacja

2

g

GMm

F

r

=

;

pot

GMm

E

r

= −

;

z

pot

R

h

mgh

E

<<

=

,

Ruch po okręgu

t

ϕ

ω

∆

=

∆

;

v

r

ω

=

;

2

2

f

T

π

ω

π

=

=

;

0

t

ω ω

ε

=

±

;

2

0

( )

2

t

t

t

ε

ϕ

ω

=

±

;

s

a

r

ε

=

;

2

d

v

a

r

=

;

2

d

mv

F

r

=

;

Ruch obrotowy

)

,

(

sin

F

r

Fr

M

r

r

∠

=

;

)

,

(

sin

p

r

pr

K

r

r

∠

=

;

2

1

n

i i

i

I

m r

=

=

∑

;

2

2

kin

I

E

ω

=

;

K

I

ω

=

;

M

I

ε

=

;

Ruch drgający

sin(

)

x

A

t

ω ϕ

=

+

;

cos(

)

v

A

t

ω

ω ϕ

=

+

;

2

2

sin(

)

a

A

t

x

ω

ω ϕ

ω

= −

+

= −

;

F

kx

= −

;

k

m

ω

=

;

2

m

T

k

π

=

;

2

l

T

g

π

=

;

2

2

pot

kx

E

=

;

Fale

v

vT

f

λ

=

=

;

ob

źr

źr

v u

f

f

v

u

±

=

m

;

Hydrostatyka

F

p

S

=

;

m

V

ρ

=

;

p

gh

ρ

=

;

W

F

gV

ρ

=

;

Termodynamika

w

Q

mc

T

=

∆

;

Q

mL

=

Q

mR

=

;

pV

nRT

=

;

A

m

N

n

M

N

=

=

p

V

C

C

R

=

+

;

Q

U

W

= ∆ +

;

'

U

Q W

∆ = +

;

W

p V

= ∆

;

1

2

1

1

Q

Q

W

Q

Q

η

−

=

=

;

1

2

1

T

T

T

η

−

=

Elektrostatyka

2

0

1

|

|

4

r

Qq

F

r

πε ε

=

;

F

E

q

=

;

0

1

4

pot

r

Qq

E

r

πε ε

=

;

pot

E

V

q

=

;

U

E

d

=

;

2

2

mv

qU =

;

Q

C

U

=

;

0

r

S

C

d

ε ε

=

;

2

2

C

CU

E =

;

1

1

1

n

i

i

C

C

=

=

∑

;

1

n

i

i

C

C

=

=

∑

;

Prąd stały

Q

I

t

=

;

U

IR

=

;

w

E

I

R

R

=

+

;

l

R

S

ρ

=

;

1

n

i

i

R

R

=

=

∑

;

1

1

1

n

i

i

R

R

=

=

∑

;

1

n

i

i

I

I

=

=

∑

;

1

1

n

m

i i

j

i

j

R I

E

=

=

=

∑

∑

;

P

UI

=

;

W

UIt

=

;

Pole magnetyczne

)

,

(

sin

B

v

qvB

F

r

r

∠

=

;

)

,

(

sin

B

l

IlB

F

r

r

∠

=

;

)

,

(

cos

S

B

BS

r

r

∠

=

Φ

;

0

2

I

B

r

µ

π

=

;

0

r

N

B

I

l

µ µ

=

;

0 1 2

2

r

I I l

F

r

µ µ

π

=

;

E

t

∆Φ

= −

∆

;

I

E

L

t

∆

= −

∆

;

2

0

r

S

L

N

l

µ µ

=

;

2

2

1

1

1

2

U

N

I

U

N

I

=

=

;

2

1

2

T

LC

f

π

π

ω

=

=

=

;

Optyka

1

1

1

f

x

y

= +

;

1

Z

f

=

;

1

2

1

2

1

1

1

1

n

f

n

R

R







=

−

+













;

1

2

2

1

sin

sin

v

n

v

n

α

β

=

=

;

sin

d

k

α

λ

=

;

Fizyka współczesna

2

E

mc

=

;

0

2

1

m

m

v

c

=

 

−  

 

;

f

hc

E

hf

λ

=

=

;

f

h

p

λ

=

;

2

2

mv

hf

W

=

+

;

B

h

h

p

mv

λ

=

=

;

1

2

n

E

E

n

=

;

2

2

1

1

1

R

m

n

λ





=

−









;

1/ 2

0

0

2

t

t

T

N

N

N e

λ

−

=

=

.

Stałe fizyczne

2

2

m

m

9,8

10

s

s

g =

≅

;

2

11

2

Nm

6, 67 10

kg

G

−

=

⋅

;

6370km

Z

R =

;

24

6 10 kg

Z

M ≅ ⋅

;

30

2 10 kg

S

M ≅ ⋅

;

23

1

6, 02 10

mol

A

N =

⋅

;

J

8, 3

molK

R =

;

2

12

0

2

C

8,85 10

Nm

ε

−

=

⋅

;

2

7

0

2

N

4

10

A

µ

π

−

=

⋅

;

8

m

3 10

s

c = ⋅

;

19

1, 6 10

C

e

−

=

⋅

;

31

9,1 10

kg

e

m

−

=

⋅

;

27

1, 67 10

kg

p

m

−

=

⋅

34

6, 6 10

Js

h

−

=

⋅

stała Rydberga

7

1

1,1 10

m

R =

⋅