Vectors
There is a great temptation to put vectors tail-to-tail when you go to add them.
May all the battles that you wage in your war against that temptation end with
your glorious triumph. Vectors add head-to-tail.
We are about to embark on the study of
Unit Vectors
What is probably the most common mistake involving unit vectors is simply leaving their
hats off. While leaving the hat off a unit vector is a nasty communication error in its own
right, it also leads one to worse mistakes such as treating ve
Integration
An integral is an infinite sum of infinitesimal terms.
An integral is an operator. I want to convey what I mean by the term operator by first
discussing an operator with which you are already familiar, namely the derivative operator. An
operat
Some Simple Algorithms1 for Calculating Derivatives
The Derivative of a Constant is Zero
Suppose we are told that
x = xo
where xo is a constant and x represents the position of an object on a straight line path, in
other words, the distance that the objec
A physics professor wishes to demonstrate that applying
the same force to two different objects over the same
distance results in a bigger impulse to the more massive
object. He sets up two horizontal tracks with two identical
carts. A string extends hori
A piston is used to keep a gas compressed in a
cylinder such that the pressure of the gas is
greater than atmospheric pressure. The piston is
on top of the gas with the face of the piston facing
downward. A person is holding the piston down.
The person re
Is it possible to warm up an ice cube
without melting it?
a) Yes
b) No
Is it possible to heat up water vapor
beyond 100C?
a) Yes
b) No
If heat flows into liquid water, and
there is no other exchange of
energy between the liquid water and
the surroundings,
If 475 J of heat flows into a 225 gram
sample of water,
a) the heat of the sample decreases by
475 J.
b) the heat of the sample increases by
475 J.
c) None of the above.
Whenever heat flows into a substance,
the temperature of that substance
increases.
a)
Two 15-meter-long hoses are being used to fill a
swimming pool. Hose 1 is attached, at one end, to a
water main. Hose 2 is attached to the other end of hose
1. Thus the water flows from the water main into hose 1,
through hose 1, into hose 2, through hose
The tank atop a water tower has the shape of a right
circular cylinder with vertical walls. To quadruple the
capacity, the tank is replaced with another tank of twice
the diameter but the same height. Extra columns, are
added to support the additional wei
What does the v (with no subscript) in the
equation
stand for?
R
=
S
a) The velocity of the source.
b) The velocity of the receiver.
c) None of the above.
What does the vR in the equation
R
=
S
stand for?
a) The velocity of the receiver
relative to
What does it mean for a wave in a string to be
reflected?
a) It reaches the end of the string and bounces
back.
b) All parts of the wave become the opposite of
what they were. All crests become troughs
and all troughs become crests.
c) A transverse wave b
What kind of equation is this?
a)
b)
c)
d)
e)
f)
g)
h)
A wave equation.
An algebraic equation.
A partial differential equation.
All of the above.
Both a and b.
Both a and c.
Both b and c.
None of the above.
What does the y stand for?
a) Position along the
What causes waves?
a) An arrangement of the elements of a
medium that is an oscillatory function
of both time and position.
b) The motion of matter through space.
c) Light.
d) Sound
e) Something oscillating.
What is a definition of a wave?
a) An arrangeme
What happens to the period of a simple
pendulum if you double the mass of the
bob?
a) The period remains the same as it was.
b) The period becomes twice what it was
c) The period becomes one-half what it was.
d) The period becomes four times what it was.
What happens to the period of an ideal mass-ona-spring system when the amplitude is doubled?
a) The period remains the same as it was.
b) The period becomes twice what it was
c) The period becomes one-half what it was.
d) The period becomes four times wha
What is impulse? Choose the one best
answer.
a) Force times time.
b) Force times distance.
c) Momentum.
d) Change in momentum.
e) Force.
f) Energy.
What is the Impulse Momentum relation?
a) Force times distance equals momentum.
b) Force times distance equ
Depicted is the potential
energy function for a
particle confined to the
x axis. Where must the
particle be in order for
the force on it to be in the +x direction?
a) At any x < x1
b) At any x > x1
c) At x = 0
d) At x = x1
e) There is no position at which
Regarding a situation in which work is done on
a massive particle: What is work? (You are
not being asked what it is equal to but what it,
by definition, is.)
a) Force along the path times the length of
the path.
b) The negative of the change in potential
The diagram shows an
object suspended vertically
by string 3 which is tied to
two other strings, string 1
and string 2. In which string
is the tension greatest?
2
1
3
m
a) String 1
b) String 2
c) String 3
d) Not enough information is given.
4
A bowling ba
Particles 1 and 2, having masses m1 = m and
m2 = 2m respectively, lie on the x axis at
(0, 0, 0) and (1.00 m, 0, 0) respectively. Where
is the center of mass?
a) Midway between the two particles.
b) Between the two particles, closer to
particle 1.
c) Betw
B
A
What is the direction of
?
a) Toward the right side of the page.
b) Toward the left side of the page.
c) Toward the top of the page.
d) Toward the bottom of the page.
e) Out of the page.
f) Into the page.
A small telescope is mounted on a ball and soc
What is the direction of the angular velocity of
the second hand of the clock on the wall in this
room?
a) Northward
b) Southward
c) Eastward
d) Westward
e) Upward
f) Downward
Axis of
Rotation
a
b
O
c
F
Which distance in the diagram above is the
moment ar
Did you do the reading assignment?
a) Yes
b) No
c) Sort of.
A person inverts a bicycle and gives the wheel
a spin. If I ask you how many revolutions it will
complete before it comes to rest, I am asking
you to find the value of:
a)
b)
c) I
d) None of th
Is it appropriate to say that a disk is spinning at
a rate of 15 m/s?
a) Yes.
b) No.
Is it possible for a particle to have a non-zero
acceleration while it is moving at a constant
speed?
a) Yes.
b) No.
A person ties a rock to the end of a piece of
string
Consider the two erasers on the whiteboard
tray. Are they exerting a gravitational force on
each other?
a)Yes.
b)No.
Consider the two erasers on the whiteboard
tray. Are they accelerating toward each other?
a)Yes.
b)No.
Consider the two erasers on the whi
Suppose you give a cart, that is at rest on a
horizontal frictionless track, a horizontal shove,
in the forward direction, with your hand. After
the cart leaves your hand:
a) The force of your hand on the cart is
forward.
b) The force of your hand on the
A board is lying flat on a floor. A person puts a brick on
the board and raises one end of the board until the
board makes an angle of 41 with the horizontal, slides
a support under that end of the board, and then lowers
the end of the board down onto the
A fully-loaded eighteen-wheel tractor-trailer rig
(a.k.a. a big truck) and a small passenger
vehicle experience a head-on collision with
each other. Which vehicle, if either, exerts a
greater force on the other vehicle, during the
collision?
a) The truck
(Demo) I launch one die forward and at the
instant of launch I drop another one from right
beside the first one.
Which die hits the floor first?
a) The launched die.
b) The dropped die.
c) Neither; both dice hit at the same time.
A boy throws a rock. It l