Formula Sheet for Homework and Exams – Page 1 of 2


U    Fcons  dx
1.
v f  v 0  a t f  t 0 
23.
2.
x f  x 0  v 0 (t f  t 0 )  12 a (t f  t 0 ) 2
24.
U g  m g (y  y 0 )
3.
x f  x 0  12 ( v 0  v f )( t f  t 0 )
25.
U s  12 k ( x  x 0 ) 2
4.
x f  x 0  v f (t  t 0 )  12 a ( t f  t 0 ) 2
26.
27.
28.
 K   U  Wnoncons
s  r
v tangential   r
29.
a tangential   r
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
v f  v 02  2ax f  x 0 
 

 F  Fnet  m a
2r
T
v
v2
a centripetal 
 2 r
r
a radial  a centripetal


p  mv

 
dp
 F  Fnet  d t



J   Fnet dt   p


P   pi


dP
  Fext
dt
2
  0  t  t 0 
31.
   0  0 (t  t 0 )  12 ( t  t 0 ) 2
32.
   0  12 (0  )( t  t 0 )
33.
   0  ( t  t 0 )  12 ( t  t 0 ) 2
 2  02  2   0 
   
35a. a  b  a b sin( )
 
a  b  a y b z  a z b y î 
35b.
a z b x  a x b z  ĵ  a x b y  a y b x k̂
34.

36.
37.
M   mi
1
1
x cm   m i x i y cm   m i y i
M
M


P  M v cm
   
a  b  a b cos()  a x b x  a y b y  a z b z
 
W  Fd
 
W   F  dx
21.
K  12 m v 2  12 m (v x  v y )
22.
K f  K i  Wnet
2
30.
38.
39.
40.
41.
42.
43.
2
I   m i ri



2
K rot  12 I 2
 
W     d
  
  r F

 dL

  I  d t
  
l  r p


L  l i


L  I
44x. m1 v1, x ,before  m 2 v 2, x ,before  m1 v1, x ,after  m 2 v 2, x ,after
44y. m1 v1, y ,before  m 2 v 2, y ,before  m1 v1, y ,after  m 2 v 2, y ,after
44z. m1 v1,z ,before  m 2 v 2,z ,before  m1 v1,z ,after  m 2 v 2,z ,after
45a. v1,f 
m1  m 2
2 m2
v1,i 
v 2 ,i
m1  m 2
m1  m 2
Rev. 08-Feb-07 G. Bedrosian
45b.
v 2 ,f 
2 m1
m  m1
v1,i  2
v 2 ,i
m1  m 2
m1  m 2
1
Formula Sheet for Homework and Exams – Page 2 of 2
46a.
46b.
47a.
47b.
48a.
48b.
49.

m m
| F | G 1 2 2
r

m m
F  G 1 2 2 r̂
r

1 | q1 | | q 2 |
| F |
4  0
r2

1 q1 q 2
F
(r̂ )
4  0 r 2

1 | qi |
| Ei |
4   0 ri 2

1 qi
E
(r̂i )
4   0 ri 2


F  qE
50.
51.
52.
1 qi
4   0 ri
U  qV
 
V    E  dx
V
V
x
V
53y. E y  
y
V
53z. E z  
z

 
54. F  q v  B
mv
55. r 
qB
53x. E x  
N 1 N
56.
1 qi q j
i 1 j  i 1 4   0 ri j
U config   
Useful Constants
(You can use the approximate values on exams.)
Universal Gravitation Constant
G  6.67310 11 N m 2 kg 2  6.67 10 11
Electrostatic Force Constant
1
 8.987551788 10 9 N m 2 C  2  9.0 10 9
4  0
Magnetic Constant
 0  4  10 7 H m 1  1.26 10 6
Speed of Light in Vacuum
c  2.99792458 10 8 m s 1  3.0 10 8
Charge of a Proton
e  1.602176462 10 19 C  1.6 10 19
Electron-Volt Conversion Constant
1eV  1.602176462 10 19 J  1.6 10 19
Mass of a Proton
m p  1.6726215810 27 kg  1.67 10 27
Mass of an Electron
m e  9.10938188 10 31 kg  9.110 31
Rev. 08-Feb-07 G. Bedrosian
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