UNIVERSITY PHYSICS II and IIA FORMULA SHEET

netF ma=�

�

dv

adt

=�

�

dr

vdt

=�

�

212o o

r r v t a t= + +� � � �

2

x

1a

2o oxx x v t t= + +

2 2 2 ( )o o

v v a r r= + ⋅ −� � �

2 2 2 ( - )x ox x ov v a x x= +

0θ θ θ∆ = −

avg t

θω =

∆∆

d

dt

θω =

-o

ω ω ω∆ = = avgt

ωα

∆∆

2

2

d d

dt dt

ω θα = =

212o o

t tθ θ ω α= + + 2 2

02 ( - )

oω ω α θ θ= +

s rθ= v rω= t

d va r

dtα= =

�

2

2 r

va r

rω= =

2

i ii

I m r=∑ 2

rigidbody

I r dm= ∫ 2+com

I I Mh=

x r Fτ =�

��

sinrF rF r Fτ θ ⊥ ⊥= = =

net

Iτ α=��

21

2K Iω=

f

i

W d

θ

θ

τ θ= ∫ P τ ω=

total final initialW K K= −

final final initial initial nonconserativeK U K U W+ = + +

comv rω=

coma rα=

x x r p r mv= =� � � �

�

l sinrp rp r pφ ⊥ ⊥= = =l

L = ∑��

l L Iω=�

�

net

d L

dtτ =

�

�

F LE

A L

∆ =

F xG

A L

∆ =

Vp B

V

∆=

( )2( ) = - ( ) ( ) = cos +m

a t x t x t x tω ω φ 1

2

fT

ωπ

= =

F kx= − 212

U kx= 2m

Tk

π=

2I

Tmg h

π=

( , ) ( )y x t h x vt= ± v fk

ωλ= =

2 k

πλ

=

( )( , ) sinm

y x t y kx tω φ= ± +

( , ) 2 cos sin2 2m

y x t y kx tφ φ

ω

= − −

TF

vµ

= 2 21

2avg mP v yµ ω=

( , ) 2 sin( ) cos( )m

y x t y kx tω=

2n

L

nλ =

1nf n f= n = 1, 2, 3, 4, 5 ….

2

Lφπ λ

∆=

Bv

ρ=

( , ) sin( )m

p x t p kx tω∆ = ∆ − ( , ) cos( )m

s x t s kx tω= − m mp v sρ ω∆ =

PI

A=

24

PI

rπ= ( )21

2 mI v sρ ω=

( )10.0 dB logo

I

Iβ

=

12

2

W10

moI −=

( )( , ) 2 cos sin2 2m avg avg

ky x t y x t k x t

ωω

∆ ∆ = − −

2 1beatf f f= −

' D

S

v vf f

v v

±= ±

cn

v=

1 1 2 2sin sinn nθ θ=

1 1 1 'i hm m

f p i p h= + = − =

sin 0, ±1, ±2, d m mθ λ= = … (constructive)

2

0

24 cos sin

2

dI I

φ πφ θ

λ

= =

sin = ±1, ±2, ±3, a m mθ λ= … (destructive)

2sin

sinm

aI I

α πα θ

α λ

= =

2 20

1

cos tanB

nI I

nθ θ= =

2I MR=

2 21 1

4 12I MR ML= +

21

2I MR=( )2 2

1 2

1

2I M R R= +

21

12I ML= 22

5I MR=

( )2 21

12I M a b= +

21

2I M R=22

3I M R=