Please indicate which of the math
subjects (if any) that you are currently
enrolled in.
1) 18.01
2) 18.01A/18.02A
3) 18.013A
4) 18.014
5) 18.02
6) 18.022
7) 18.023
8) 18.03
9) no math subject or higher level
We just measured the speed of light an

Newtons Laws of Motion
8.01T
Sept 20, 2004
Newtons First Law
Every body continues in its state of rest, or
of uniform motion in a right line, unless it is
compelled to change that state by forces
impressed upon it.
Newtons Second Law
The change of motion

Hookes Law and Circular
Motion
8.01T
Sept 29, 2004
Stretching a Spring
Suppose we have a spring whose
relaxed length is x0, and stretch it
to a length xF.
According to Hookes law, the
restoring force will be proportional
to the amount of stretch,
Fspring

Circular Motion
and Universal Law of
Gravitation
8.01t
Oct 4, 2004
Summary: Circular Motion
arc length
s = R
tangential velocity
ds
d
=R
= R
v=
dt
dt
dv
d 2
tangential acceleration a =
= R 2 = R
dt
dt
v2
2
= R
centripetal acceleration ar = v =
R
Circ

Problem Solving Strategies:
Static Equilibrium
8.01t
Oct 8, 2003
Static Equilibrium
(1) The sum of the forces acting on the rigid
body is zero
G
G
G
G
Ftotal = F1 + F2 + . =
0
(2) The vector sum of the torques about any
point S in a rigid body is zero
G

Circular Motion
8.01T
Sept 27, 2004
Position and Displacement
Position vector of an object
moving in a circular orbit of
radius R
G
Change in position r
between
time t and time t+t .
Position vector is changing in
direction not in magnitude.
Magnitude o

Problem Solving Strategies:
Work and the Dot Product
8.01t
Oct 15, 2003
Class Problem 1
Work done by Gravity Near the Surface of the
Earth
Consider an object of mass m near the surface
of the earth falling directly towards the center of
the earth. The gr

Potential Energy and
Conservation of Energy
8.01t
Oct 18, 2004
Conservative Forces
Definition: Conservative Work
Whenever the work done by a force in
moving an object from an initial point to a
final point is independent of the path, then
the force is ca

Cross Product, Torque, and
Static Equilibrium
8.01t
Oct 6, 2004
Cross Product
The magnitude of the cross product
A B = AB sin
0
Direction of Cross Product
Area and the Cross Product
The area of the parallelogram equals the
height times the base, which

Problem Solving Strategies:
Simple Harmonic Oscillator
and Mechanical Energy
8.01t
Oct 22, 2004
Modeling the Motion: Newton s
Second Law
Equation of Motion:
d2x
: kx = m
i
dt 2
Possible Solution: Period of
oscillation is T
Position
2
x = Acos( t)
T

Applying Newtons Second
Law
8.01T
Sept 22, 2004
Reference Frame
Coordinate system with an observer placed at origin is
a reference frame in which the position, velocity,
and acceleration of objects are mathematically
defined
Relative Reference Frames
T

Exam Three Momentum Concept Questions
Isolated Systems
4. A car accelerates from rest. In doing so the absolute value of the car's
momentum changes by a certain amount and that of the Earth changes by:
1.
2.
3.
4.
a larger amount.
the same amount .
a smal

Problem 1: Square Wave (integral)
Which of the following graphs below is the
integral of the above square wave?
1)
2)
3)
Problem 2: Sine Wave (derivative)
Which of the following graphs below is the
derivative of the above sine wave?
1)
2)
3)
Problem 3: Tr

Problem 1:
A constant force is exerted on a cart that is
initially at rest on an air track. Friction
between the cart and the track is negligible.
The force acts for a short time interval and
gives the cart a certain final speed. To reach
the same final

Problem 1
A person simultaneously throws two objects in the air. The
objects leave the persons hands at different angles and
travel along the parabolic trajectories indicated by A and B
in the figure below. Which of the following statements best
describes

In-Class Problem 7: Law of Addition of Velocities
Suppose two cars, Car A, and Car B, are traveled along roads that are perpendicular to
each other. An observer is at rest with respect to the ground. A second observer is in Car
r
A. According to the obser

Problem 1
An object goes from one point in space
to another. After it arrives at its
destination, its displacement is:
1) either greater than or equal to
2) always greater than
3) always equal to
4) either smaller than or equal to
5) always smaller th

1. You are a passenger in a racecar
approaching a turn after a straight-away. As
the car turns left on the circular arc at
constant speed, you are pressed against the
car door. Which of the following is true
during the turn (assume the car doesn't slip
on

1. A ball is given an initial horizontal
velocity and allowed to fall under the
influence of gravity, as shown below.
The work done by the force of gravity on the
ball is:
1.positive
2.zero
3.negative
2. A comet is speeding along a hyperbolic
orbit towa

1. A ladybug sits at the outer edge of a
merry-go-round, and a gentleman bug sits
halfway between her and the axis of
rotation. The merry-go-round makes a
complete revolution once each second. The
gentleman bug's angular speed is
1.half the ladybug's.
2.t

1. In part (a) of the figure, an air track cart
attached to a spring rests on the track at the
position xequilibrium and the spring is relaxed. In
(b), the cart is pulled to the position xstart and
released. It then oscillates about xequilibrium.
Which gr

r
Question 1: Consider two vectors rP ,F = x
i
r
i
with x > 0 and F = Fx + Fz k with Fx > 0
r
r
and Fz > 0 . The cross product rP ,F F
points in the
1)
+ x-direction
2)
-x-direction
3)
+y-direction
4)
-y-direction
5)
+z-direction
6)
-z-direction
7)
None o

1. Which of the following
functions x(t) of the variable t
have a second derivative which is
proportional to the negative of
the function
d2x/dt2 ~ - x
1. x(t) = (1/2)at2
2. x(t) = Aet/T
3. x(t) = Ae-t/T
4. x(t) = Acos(2/T)t)
2. The first derivative v =

Understanding Graphs of Motion
Name and section number: Connor Hoeckele Section 7
Partners name and section number: Reese Petersen Section 7
1. To demonstrate your ability to acquire data and follow the motion templates of Parts I and II,
please copy and