This preview shows page 1. Sign up to view the full content.
FORMULA SHEET
You may tear this sheet out of the exam — you do not have to hand it in with the rest of your exam.
R
x
=
A
x
+
B
x
,
R
y
=
A
y
+
B
y
,
R
z
=
A
z
+
B
z
(components of
!
R
=
!
A
+
!
B
)
!
A
=
A
x
ˆ
i
+
A
y
ˆ
j
+
A
z
ˆ
k
,
!
B
=
B
x
ˆ
i
+
B
y
ˆ
j
+
B
z
ˆ
k
!
cos
cos
B
A
B
A
!
!
!
!
=
=
"
AB
(definition of the scalar (dot) product)
z
z
y
y
x
x
B
A
B
A
B
A
+
+
=
!
B
A
!
!
(scalar (dot) product in terms of components)
C
=
AB
sin
(magnitude of
!
C
=
!
A
!
!
B
)
C
x
=
A
y
B
z
!
A
z
B
y
C
y
=
A
z
B
x
!
A
x
B
z
C
z
=
A
x
B
y
!
A
y
B
x
(components of
!
C
=
!
A
!
!
B
)
t
x
t
t
x
x
v
x
!
!
=
"
"
=
"
1
2
1
2
av
(average velocity, straightline motion)
dt
dx
t
x
v
t
x
=
!
!
=
"
!
0
lim
(instantaneous velocity, straightline motion)
t
v
t
t
v
v
a
x
x
x
x
!
!
=
"
"
=
"
1
2
1
2
av
(average acceleration, straightline motion)
dt
dv
t
v
a
x
x
t
x
=
!
!
=
"
!
0
lim
(instantaneous acceleration, straightline motion)
t
a
v
v
x
x
x
+
=
0
(constant acceleration only)
2
0
0
2
1
t
a
t
v
x
x
x
x
+
+
=
(constant acceleration only)
)
(
2
0
2
0
2
x
x
a
v
v
x
x
x
!
+
=
(constant acceleration only)
t
v
v
x
x
x
x
!
"
#
$
%
&
+
=
’
2
0
0
(constant acceleration only)
dt
a
v
v
t
x
x
x
!
+
=
0
0
!
+
=
t
x
dt
v
x
x
0
0
k
j
i
r
ˆ
ˆ
ˆ
z
y
x
+
+
=
!
t
t
t
!
!
=
"
"
=
r
r
r
v
!
!
!
!
1
2
1
2
av
(average velocity vector)
dt
d
t
t
r
r
v
!
!
!
=
=
!
"
"
"
0
lim
(instantaneous velocity vector)
dt
dx
v
x
=
dt
dy
v
y
=
dt
dz
v
z
=
(components of instantaneous velocity)
t
t
t
!
!
=
"
"
=
v
v
v
a
!
!
!
!
1
2
1
2
av
(average acceleration vector)
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Fridluund
 Physics

Click to edit the document details