WHAT IF …
PRS
accelerating
pendulum
WE SAW
A PENDULUM HANGING
THIS WAY
What could we conclude about our motion?
1) We are moving to the right.
2) We are accelerating to the right.

3) We are moving to the left.
4) We are accelerating to the left.
5) Not enough information.
6) I have no idea.
Physics 151
1
Tcos -mg = 0
Accelerating
Tcos = mg pendulum
Vertical:
solution
Horizontal: Tsin = ma
Take the ratio:
Tsin/ Tcos = tan = a/g
a = g tan
mg

T
’
a
mg
This picture might also be explained by
an additional gravitational force pulling
to the left.
Physics 151
2
Plant and turntable
Plants normally grow up.
1
What about a plant grown
on a rotating turntable?
Which way is “up”, i.e.,
which way will it grow?
2
1) Straight up
2) somewhat inward
3) somewhat outward
3
Physics 151
3
Wheat roots and shoots
Wheat grown on a rotating turntable
- new shoots grow inward.
- roots grow outward.
Grown at radius = 0.125 m,
and 1.3 rev/s for 5 days in
the dark.
v = 2pr x 1.3/s = 1.02 m/s
ac
ac = v2/r = 8.3 m/s2 toward center
g
40o angle between g and geff
geff
Physics 151
4
Inertial Frames
An inertial frame is one in which
Newton’s laws hold.
In an inertial frame, a ball gently
released stays floating in the same spot.
A ball with an initial velocity continues
in a straight line. Starlight from a
distant star travels in a straight line
across the room.
Physics 151
Imagine Professor Einstein
in his laboratory deep in
space, far from any stars.
This is an
inertial frame!
5
Inertial Frames II
What if the laboratory were moving
with constant velocity relative to the
star?
The ball would still appear to float in
the same spot. The light would still
travel in a straight line, but to Albert, it
would travel at a different angle.
Physics 151
V
This is still an
inertial frame!
6
Accelerated frames
Suppose Albert’s laboratory were
accelerating…
The ball would fall to the floor.
The light beam would appear to bend
(although probably only a tiny amount).
a
This is NOT an
inertial frame!
Physics 151
7
Accelerated frames II
If a = 9.8 m/s2,
what would this
remind you of?
The accelerated lab looks
just like a lab on Earth.
a
Physics 151
8
The Equivalence Principle
An accelerated frame is
equivalent in all respects
to a gravitational field.
Physics 151
9
Equivalence principle II
…which leads to a very important conclusion.
Light should bend in a
gravitational field.
Physics 151
10
Eddington eclipse
In May 1919, the Royal Society and the
Royal Astronomical Society sent two
expeditions to Sobral, Brazil and Principe,
W. Africa to take measurements during a
solar eclipse.
The idea: measure the apparent
location of stars during the
eclipse to see if the starlight
deviated from its usual straight
path as it passed close by the
sun.
Physics 151
11
Eddington eclipse II
Star field when the
sun is elsewhere.
Star field during eclipse.
The deviations show starlight being affected by gravity!
Physics 151
12
Eddington
IIIfrom Campbell to Einstein,
Telegram
telling him about the results of the
1922 Australian eclipse
measurements.
New York Times
May 30, 1919
"Lights Askew in the Heavens. Men of
Science More or Less Agog; Einstein's
Theory Triumphs."
Physics 151
13
Gravitational Lenses
Big Mass
Distant
Source
Light from a distant source can travel more than one path
around a source of gravity to get to an observer on Earth.
There appears to be more than one source, or the source is distorted.
If the source, mass and Earth are
all exactly in line the source will
appear to be spread into a ring.
View without
gravity.
Physics 151
View with gravity.
14
HST Gravitational Lenses
If source, mass and Earth are not exactly in a straight line,
multiple images or partial arcs are common.
Physics 151
15
Why are black holes black?
Artist’s impression
of black hole.
Physics 151
16
End
Physics 151
17
Physics 151
18
Inertial Frames
Recall that an inertial frame is one
in which Newton’s laws hold.
(The surface of the Earth is not an
inertial frame.)
In an inertial frame, a ball gently
released stays floating in the same spot.
A ball with an initial velocity continues
in a straight line. Starlight from a
distant star travels in a straight line
across the room.
Physics 151
Imagine Professor Einstein
in his laboratory deep in
space, far from any stars.
This is an
inertial frame!
19
Inertial Frames II
What if the laboratory were moving
with constant velocity relative to the
star?
The ball would still appear to float in
the same spot. The light would still
travel in a straight line, but to Albert, it
would travel at a different angle.
Physics 151
V
This is still an
inertial frame!
20
Accelerated frames
Suppose Albert’s laboratory were
accelerating…
The ball would fall to the floor.
The light beam would appear to bend
(although probably only a tiny amount).
a
This is NOT an
inertial frame!
Physics 151
21