БИБЛИОГРАФИЧЕСКИЙ СПИСОК

111

ПРИЛОЖЕНИЕ 1

Некоторые формулы курса общей физики

1. Кинематика

v =

S

at

= dv

аn

= v2

t

dt

R

a = at + an

a = a2t + an2

a

= v

t

S = vo t + at2

v = vo + at

ω= dϕ

2

dt

ϕ = ω t + εt2

ω=2πn=2π/T

n=1/T

o

2

an = v2 = r ω2

v=ω r

at = r ε

x=x0 sin(ω0t+ϕ0)

r

a = r

ε2 +ω4

v = ωo x0 cos(ωo t + ϕo )

ω=2π/T=2πn

a = dv = −ω 2x

dt

o

2. Динамика

p=mv

dp

n

G

F= ma

= ∑Fi

dt

i=1

Fтр =μ Fнд

F12=-F21

Fуп = −kx

M = F A

M=[r×F]

I= m r2

Iz=I0+md2

L = p A

L=Iω.

G

G

dL0

G

M

M=Iε

ε =

I

dt

= Mвн

G

G

dL

M dt=dL

dω

=

M = I

dt

dt

ω = k

ν = 1 k

T = 2π m

0

m

2π

m

k

T = 2π

I

Tм = 2π

A

Lпр=I/mA

mgA

g

x = x0 e−βt

sin(ωt +ϕ0 )

β=r/(2m)

ω=

ω02 −β2

T =

22 π

2

D =eβT

λ=lnD=βT

ω −β

0

x0

=

F0 / m

tgϕ =

2βω

ω

= (ω2

− 2β2 )

[(ω2

−ω2 )+ 4β2ω2

]

ω2 −ω2

р

0

0

0

3. Работа, энергия, мощность, законы сохранения

W

= mv2

W

=

I ω2

W =

p2

k

2

k

2

k

2m

W = −γ

Mm

=

W = kx02

cos2 (ω t + ϕ

)

Mm

p

R + h

W = −γ

k

2

0 0

p

r

= −γ Mm + mgh

R

W

=

kx2

Wp = Wp0

− Wp

= mgh

W =

kx02

p

2

2

G

G

r2

1

1

A =

∫

F dr

A = ∫dA = γMm

−

A = M ϕ

r2

r

r1

r1

A = −

kx2

N

= A /

t

N = M ω

2

u1 = (m1 − m2 )v1 ± 2m2v2

m1

+ m2

W = Wk

+ Wp = const

u2 =

(m2 − m1 )v2 ± 2m1v1

k =

u

m1

+ m2

v

u = m1v1 + m2 v2

m + m

2

1

4. Поле тяготения

ϕ

g = γ

M

ϕ =

Wp

= −γ

M

gr = −

r2

m

r

r

G

= γ

Mm

v =

gR

v =

2gR

F

2

r0

1

2

5. Кинематика и динамика жидкостей

FA = ρgV

F = η v S

η= η0

e−kT

U

z

ρv2

1

1

+ρgh + p = const

p=ρgh

+

2

p = σ

R1

R2

h =

2σ cosθ

h =

2σ cosθ

ρgr

ρgd

113

6. Элементы СТО

u' = u − v

A= A0 1−β2

τ0 = τ 1−β2

vu

1− c2

m(v) =

m0

G

G

=

m0 v

Wk = m0c

2

1

−

1

−β

2

p = m v

1−β

2

1−β2

1

m =

E

E = m2c4 = c p2 + m2c2

p =

1

Ek2 + 2Ek m0c2

c2

0

c

7. Молекулярная физика и термодинамика

μ=m0 NА

pV = 1 N'm vкв2

p

= 1

n0mvкв2

3

3

p = n

kT

p = 2 n

E

pV = m RT

0

3

0

μ

E = i kT

U = m i

RT

cv

= i R

2

μ 2

2 μ

cp = i + 2 R

Cv

= i

R

Cp = i + 2 R

2

μ

2

2

γ = Cp Cv = (i + 2) i.

v

=

2kT

1 2

=

2RT

1 2

v =

8kT

1 2

=

8RT

1 2

в

μ

πμ

m

πm

v

kT

Z =

v

1 2

1 2

λ = Z

= 21 2 πd2p

λ

Z = 2

noσ v

=

2

no

σ v

σ=πd2

p = po exp(−μgh RT)

δQ =dU +δA

A = m RTln(V2

V )

Q = Cp T

U = C

v

T

μ

1