MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01
Spring 2005
QUIZ 8
FORMULA SHEET
Quiz Date: Friday, April 1, 2005
For motion in one dimension:
v
av
≡
∆
x
∆
t
Average velocity;
v
≡
d
x
d
t
Instantaneous velocity;
For motion in three dimensions:
v
≡
d
r
d
t
;
a
≡
d
v
d
t
=
d
2
r
d
t
2
;
r
(
t
1
) =
r
0
+
t
1
0
v
d
t
;
v
(
t
1
) =
v
0
+
t
1
0
a
d
t .
For
constant
acceleration
a
, if
r
=
r
0
and
v
=
v
0
at time
t
= 0, then
v
(
t
) =
v
0
+
a
t
r
(
t
) =
r
0
+
v
0
t
+
1
2
a
t
2
.
For onedimensional motion with constant acceleration
a
:
v
2
=
v
2
0
+ 2
a
(
x
−
x
0
)
.
For circular motion at constant speed
v
:
a
=
v
2
r
,
where
r
is the radius of the circle, and the acceleration is directed towards the center of
the circle.
If an object has position
r
and velocity
v
, its position and velocity relative to an
observer with position
r
0
and velocity
v
0
are given respectively by
r
=
r
−
r
0
,
v
=
v
−
v
0
.
Average velocity and acceleration are given by
v
average
≡
∆
r
∆
t
,
a
average
≡
∆
v
∆
t
.
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Mass, Acceleration, and Force:
F
=
m
a
(Newton’s second law);
F
=
−
GMm
r
2
ˆ
r
(the gravitational force between two particles);
F
=
1
4
π
0
Qq
r
2
ˆ
r
(the electrostatic force between two particles);
F
x
=
−
kx
(Hooke’s law);
where
ˆ
r
is a unit vector pointing from the particle which is the source of the force,
toward the particle on which the force is acting.
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 Spring '03
 Rivest
 Force, Kinetic Energy, Potential Energy, dt dt, dt dv dt

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