Have I told you how much I hate these people? - Mike Malloy. It is every thinking person’s responsibility not to side with his or her executioners. - Albert Camus. Popular democracy anywhere threatens fascism everywhere. - The Scallion. A fascist junta of neocons using George W. Bush as its shill has taken over America by bloodless coup. What will it take for us to stage a revolution and take our country back? - Dot Calm. Drive a hybrid. Leave a lighter footprint on the planet. - Dot Calm.
Like Granny D, I have watched my own beloved country change, and I am angry beyond words about what I see. I grew up seeing America as the equivalent of the movie good guy, the hero in the white hat who came to the rescue of those in need around the world. I have watched in silent horror as the corporations, the captains and the kings of industry, used a comparatively small outlay of cash to buy the Republicans to use as their shills. George W. Bush is the puppet cowboy-king of shills, the proverbial emperor with no clothes. Every day, I watch these evil men legalize, legitimize, and institutionalize robbing the poor to pay the rich. They are carving up America like a giant carcass and doling out choice chunks of its meat to themselves and their cronies. Since the Democrats have been sipping at the same corporate teat where the Republicans have been gorging for the past generation, the fascists are free to do their worst; there is no longer any opposition. There is no one left to stand up for the rights of the American people, the Constitution, or the democracy, which I fear will be replaced by a fascist dictatorship in my lifetime. Wake up, America: we need a REVOLUTION NOW!
Over
the course of his brief, polarizing career in electoral politics, Texas
Sen. Ted Cruz has been called many names, especially by liberals.
“Dirty Syrup Guzzler” (Jon Stewart). “Creature from the Nether Regions” (Cher). “The Most Dangerous Canadian in America” (the Huffington Post).
Yet
so far the most indelible description of Cruz has come from a fellow
conservative. In 2013, when Cruz decided to protest U.S. drone policy by
filibustering the nomination of incoming CIA chief John Brennan, John
McCain told reporter Jon Ward — now a senior political correspondent for
Yahoo News — that his junior colleague was a “wacko bird.”
By
using that particular moniker, McCain was, in effect, dismissing Cruz
as both flighty and crazy. And for the most part that is exactly how the
Texan has been characterized in both the press and the public
imagination since he alighted on Washington, D.C., nearly three years
ago and immediately set about trolling his fellow Republicans and hijacking the legislative process:
as an irresponsible far-right demagogue prone to behave in irrational,
counterproductive ways. Cruz’s showy obstructionism suffers from “basic
logic problems” and “just doesn’t make sense,” wrote the
Atlantic’s Molly Ball in 2013. “Zealot leaders” like Cruz “forget that
the key to leadership is essentially getting results by moving agendas
ahead,” added Inc. magazine.
Many pundits were skeptical when, in a speech at Virginia’s evangelical Liberty University on March 23 , Cruz became the first Republican to announce he was entering the 2016 presidential race. As the New York Times’ Nate Cohn put it at the time, “The most interesting question about Mr. Cruz’s candidacy is whether he has a very small chance to win or no chance at all.”
But here’s the thing: Ted Cruz has always been more of a mastermind than a wacko bird.
Every
politician plans, plots or schemes (depending on how pejorative you
want to be about it); that’s part of the job. But not every politician
is a prodigy at it.
Ted
Cruz is. Since adolescence, Cruz has invested the vast majority of his
time, energy and boundless ambition in endeavors that require and reward
long-term strategic thinking — aka the fine art of making a plan and
sticking to it. He honed his skills as a champion debater at Princeton
University. He perfected them as one of the most effective appellate
lawyers in the country. He relied on them during his first long-shot
race in Texas. And now he is deploying them in the national arena as a
senatorial troublemaker and presidential candidate. With the possible
exception of Frank Underwood, the fictional star of Netflix’s House of Cards,
there may be no shrewder, more calculating figure in American politics
than Cruz — and so far, nearly all his calculations have paid off.
“Ted
has a remarkable talent for strategic thinking,” says Charles Cooper,
co-partner of the D.C. firm where Cruz first practiced law. “He
understands that the things you say and do today can lay the groundwork
for the things you want to accomplish in the next breath, a year from
now or beyond. That’s crucial in both law and politics.”
A
look back at Cruz’s life as a strategic phenom shows how he plotted his
way to his current perch as a potential president — and hints at what
his next move might be.
It also demonstrates how he can be defeated.
***
Ted Cruz as a baby with his father, from a campaign ad.
Rafael
Edward Cruz was 17 years old when he arrived at Princeton University.
He had already abandoned his family nickname “Felito” in favor of the
more American-sounding “Ted.” He had already read Adam Smith,
free-marketer Milton Friedman and libertarian hero Ludwig von Mises. He
had already spent hundreds of hours studying the Constitution, the
Federalist Papers and other founding documents at Houston’s Free
Enterprise Institute, where his father had signed him up for classes
four years earlier. And he was already a die-hard Republican.
“We all grow more conservative as we age,” a fellow student remembers Cruz saying at the time. “Why wait to grow old when you can be conservative now?”
In
fact, Cruz — who was born in Canada to an American mother and a Cuban
father — was so driven that by the time he started college he had
already looked into whether he would be allowed to serve as president
someday.
“He knew what he wanted,” Cruz’s Princeton friend Michael Lubetzky told the Washington Post.
“We talked a lot about the ‘natural born’ clause in the Constitution.
Ted said when he was a kid, he’d checked to see if he’d be eligible.”
Cruz
tried to launch his political career at Princeton. Over the course of
four years, he campaigned for student government, class president and
debate-panel president, among other offices. He almost always lost. The
problem, according to Cruz’s classmates, was simple, and not solved by
strategic thinking: Many of his peers found him unlikable. Among the
words they have used to describe the collegiate Ted Cruz in the decades since: “abrasive,” “intense,” “strident,” “crank,” “arrogant” — even “creepy.”
Editor's note: I agree with all of those, but I'd definitely go with "creepy."
In
the most basic sense, democracy is a popularity contest. But while most
politicians learn to be likable in order to get elected, Cruz has shown
from an early age that he’s unwilling — or perhaps just unable — to
conceal the qualities that his colleagues tend to camouflage when
seeking votes: the narcissism, the scheming, the blatant lust for power.
Consider how Cruz is cozying up to Trump (and, to lesser degree,
Carson) while at the same time all but admitting that the only reason
he’s doing it is to siphon off supporters when the frontrunners
inevitably go belly-up. It’s almost as if he has decided that he’s so
skilled at outmaneuvering the competition that his maneuvering itself
should be a selling point—a more important qualification than whether or
not he’s likable.
Outside
the classroom, Cruz achieved his greatest success at Princeton as a
member of the Whig-Cliosophic Society, the school’s home for debate; he
joined as a freshman, spent nearly every weekend on the road with the
team and quickly became the number one collegiate debater in the nation.
While
Cruz was legendary for his ability distill an argument to its simplest
point, what he said was often secondary to how he said it. Often this
meant bedeviling his opponents, and beguiling the student judges, with
an array of tactical tricks developed during the late-night postgame
recaps that Cruz forced his debating partner to participate in. “If we
were fighting against us, what would we have done to win?” Cruz would ask. “What could we have done to get more points?”
What truly distinguished Cruz, though, was his knack for strategy.
“It’s
chess to him,” says Sacha Zimmerman, a Columbia debater who knew Cruz
from the circuit.
“He’s a machine. He sees all these options — plan Bs
and Cs. ‘If this move happens, then this move happens.’”
Instead of responding to his opponents’ arguments, Zimmerman explains, Cruz would simply “reframe the whole debate.”
“Cruz
thought of angles ahead of time and found ways make them work for
whatever the theme of the debate was,” she says. “Most of us did not do
that. We’d show up and find out that we were supposed to be talking
about ‘ideas of freedom’ or whatever, and in our 10 minutes of prep time
we’d come up with what we wanted to say. But Cruz would already have
his approach thoroughly mapped out, and he would have already thought
through every alternate argument too. It was huge advantage.”
Cruz,
flanked by Carly Fiorina and New Jersey Gov. Chris Christie, during
last month’s presidential debate in Boulder, Colo. (Photo: Justin
Sullivan/Getty Images)
To
see Cruz execute his signature maneuver, rewatch last month’s CNBC
debate in Boulder, Colo. At one point, moderator Carl Quintanilla asks
Cruz whether his opposition to the recent bipartisan budget deal shows
that he is “not the kind of problem solver American voters want.” In
response, Cruz doesn’t just decline to answer; instead he transforms
Quintanilla’s rather docile question into damning proof of the
mainstream media’s alleged bias against Republicans.
“The
questions that have been asked so far in this debate illustrate why the
American people don’t trust the media,” Cruz thunders. “This is not a
cage match. And you look at the questions: ‘Donald Trump, are you a
comic book villain?’ ‘Ben Carson, can you do math?’ ‘John Kasich, will
you insult two people over here?’ ‘Marco Rubio, why don’t you resign?’
‘Jeb Bush, why have your numbers fallen?’ How about talking about the
substantive issues people care about?”
The audience roars.
According to Frank Luntz, who has been focus-grouping presidential
debates for more than 15 years, Cruz’s response received a 98 out of
100, the most favorable rating ever recorded.
Yet
on second viewing, what’s striking about Cruz’s pivot is how
premeditated it sounds. Cruz’s tell is the way he was able to rattle
off, with remarkable accuracy, the most unflattering questions his
rivals had already been asked. It seems clear that Cruz arrived in
Boulder planning to spend the first part of the debate making a mental
list of every “biased” query for later use. By the time Quintanilla got
around to him, he was ready to strike.
***
Cruz
continued to strategize at Harvard Law. His byline — or, rather,
bylines — were telling. When he wrote for the Harvard Latino Law Review,
a journal that he co-founded, Cruz signed his articles “Rafael E.
Cruz.” Elsewhere, such as in the conservative Harvard Journal of Law and
Public Policy, “R. Ted Cruz” was his moniker of choice. Conversations
with Cruz’s fellow law students, especially those who served with him on
the prestigious Harvard Law Review, suggest that Cruz wasn’t always the
most reliable contributor; he was widely seen as being too busy
volunteering as a research assistant for various influential professors –
the kind who could later write him recommendation letters – to bother
with less urgent matters.
Cruz’s
main objective in Cambridge was clear: He wanted to win a clerkship
with Supreme Court Chief Justice William Rehnquist. (“From day one,” his
study partner has recalled,
“that was his tangible, near-term goal.”) Everyone knew that Rehnquist,
a devoted tennis player, preferred to hire clerks who knew their way
around the court. But Cruz had barely ever picked up a racket.
“Would you be willing to play tennis with me and my other clerks?” Rehnquist asked Cruz when they met for a job interview.
“I should tell you I’m not very good,” Cruz claims to have replied.
What
Cruz doesn’t mention — and what several classmates remember him being
“very open” about at the time — is that he had already described himself
as a tennis player on his application for the clerkship.
Either
way, Cruz got the job. To prepare, he spent the next several months
cramming with a tennis coach. But the lessons didn’t seem to help: Cruz
still bombed in his first doubles match with Rehnquist, whose team won
in straight sets — 6-0, 6-0, 6-0.
In
1998, Cruz moved on to a boutique Washington, D.C., firm then known as
Cooper & Carvin; he was the first associate hired. “Ted had a golden
résumé,” says Mike Carvin today. (Carvin, who has been called “the hard right’s best advocate,” is the lawyer who earlier this year argued against Obamacare before the Supreme Court in King v. Burwell.)
“We figured he would be a very good candidate to succeed in private
practice as well.” Cruz’s plotting had paid off yet again.
From
the beginning, Cruz proved particularly adept at the kind of law that
he would go on to practice for the next decade: appellate litigation.
This is key to understanding Cruz. As legal journalist Jeffrey Toobin wrote last year in the New Yorker,
“Trial lawyers, civil or criminal, are often brought into cases when
there are compromises to be made; much of their work winds up involving
settlements or plea bargains. But appellate litigators, like Cruz,
generally appear after the time for truce has passed. Their job is to
make their best case and let the chips fall where they may.”
For
Toobin, Cruz’s specific brand of legal expertise explains “the kind of
politician Cruz has become — one who came to Washington not to make a
deal but to make a point.”
That’s
undoubtedly true. But there’s another difference between trial lawyers
and appellate litigators that’s just as important in explaining Cruz.
Trial lawyers argue over facts: Was the traffic light green or red? Appellate
litigators, meanwhile, argue over the law itself — what it says, what
it means, how it applies to the case at hand. To be a good appellate
lawyer — and Cruz, according to James Ho, his successor as Texas
solicitor general, is “easily the best appellate lawyer in the state of
Texas and truly one of the best appellate lawyers in the nation” —
knowing the rules very, very well is essential. But you also have to
know how to make them work in your favor.
At
Cooper & Carvin, the biggest test of Cruz’s burgeoning talent for
appellate law was a case involving two sitting U.S. congressmen: Boehner v. McDermott.
A Florida couple had used a police scanner to eavesdrop on Rep. John
Boehner of Ohio discussing House Speaker Newt Gingrich’s ongoing ethics
troubles during a conference call with Gingrich and other Republican
leaders. The couple then gave an audiotape of the call to Democratic
Rep. John McDermott, chair of the committee investigating Gingrich, and
he, in turn, gave it to various newspapers. Boehner sued. Initially, a
district court ruled that McDermott had not broken the law, arguing that
even though someone else had recorded the call illegally, McDermott—
the middleman — was protected by the free speech clause of the First
Amendment because the conversation on the tape was a matter of public
concern.
Boehner
appealed, and that’s where the 28-year-old Cruz came in. As “the key
architect of our legal strategy,” according to Carvin, Cruz reframed the whole debate,
urging his bosses to question whether leaking a tape to a newspaper
even qualified as speech in the first place. This time, the court sided
with Boehner. According to its ruling, McDermott had merely “caused a
copy of the tape” to be given to the press — meaning that while his
behavior may have conveyed a message, it was essentially conduct and
therefore not protected by the First Amendment.
As
effective as Cruz was at Cooper & Carvin, however, his superiors
could already sense that he was mulling his next move. “It was clear,”
Cooper says. “He was very animated about public policy. He was very
interested in politics himself. But the thing that was unusual about Ted
wasn’t his interest. It was his real potential talent as a politician.”
***
More
than a decade before he would run for office himself, Cruz joined
George W. Bush’s presidential campaign as a domestic policy adviser.
When the election devolved into a chaotic clash over Florida’s hanging
chads, Cruz, who has described himself as “the only practicing
constitutional litigator” on staff, was tapped to facilitate
communication and maintain consistency across all seven of Bush’s legal
teams. Again Cruz was put in a key strategic position — and again he
excelled. “It was incredibly fast-paced and very difficult,” says
Carvin, who, recruited by his former employee, wound up representing
Bush before the Florida Supreme Court. “And Ted was always analyzing the
various challenges in a very sophisticated, savvy way.”
Yet
Cruz’s savviness had its limits. His strategic thinking may have been
helpful to Bush in court, but after hours, Cruz couldn’t seem to turn it
off. According to a report in GQ,
Cruz so frequently sent “mundane work emails in the middle of the
night” that his colleagues began to suspect him of “writing them ahead
of time and programming his computer to send while he was asleep” in
order to look like he’d been working around the clock. He would also
issue regular updates on his accomplishments that one recipient likened
to “the cards people send about their families at Christmas, except
Ted’s were only about him and were more frequent.” After the election,
many of Cruz’s campaign colleagues were rewarded with plum White House
jobs, and Cruz was expecting the same. But once again his machinations
had rubbed too many people the wrong way. He was exiled to the Justice
Department and later the Federal Trade Commission instead.
Then Texas Solicitor General Ted Cruz and Texas Attorney General Greg Abbott arrive outside federal court in Austin, Texas, in 2006 to argue a case involving congressional redistricting. (Photo: Harry Cabluck/AP)
It
wasn’t long, however, before Cruz would get another chance to put his
strategic skills to use.
Down in Texas, newly elected Attorney General
Greg Abbott had resolved to build the most aggressive AG operation in
the country — and in Cruz, whom he appointed solicitor general in 2002,
Abbott found the perfect lieutenant. The pair scoured the country for
fights brewing between the states and Washington, D.C., then inserted
Texas into the proceedings whenever possible. In doing so, Cruz and
Abbott were practicing a time-honored tradition; AGs have long targeted
cases that can help them advance their own philosophical and electoral
interests. Cruz and Abbott were just being particularly bold about it.
Cruz
had found his calling. As solicitor general, he wound up arguing nine
cases before the U.S. Supreme Court, more than any practicing lawyer in
Texas and any current member of Congress. He won five and lost four. But
while Cruz’s losses were relatively minor, his victories were
momentous. Cruz’s successor, James Ho, who refers to the senator as his
“mentor,” points to two in particular as examples of Cruz’s strategic
genius.
The first is a case that Cruz has made a central part of his stump speech ever since he started running for the Senate in 2011: Medellín v. Texas.
The facts were never in dispute. Jose Medellín, a Mexican citizen, was
on death row for the rape and murder of two teenage girls in Houston; he
had confessed to the crime immediately after his arrest. But because
U.S. authorities had failed to inform Medellín and 50 other similarly
situated Mexican nationals of their right to seek legal assistance from
the Mexican government, the judicial arm of the United Nations was now
calling for their cases to be reopened — and the Bush administration was
agreeing.
Medellín
looked unwinnable. “From a strategic standpoint, on the other side were
literally the president of the United States, the International Court
of Justice and numerous foreign countries,” says Ho. “That’s quite a
formidable wall of opposition.”
But
Cruz, as always, had a plan. He would, yet again, reframe the whole
debate. “In both law and politics, I think the essential battle is the
meta-battle of framing the narrative,” Cruz has explained. “The other side’s narrative in Medellín
was very simple and easy to understand. ‘Can the state of Texas flout
U.S. treaty obligations, international law, the president of the United
States and the world? … When Justice Kennedy comes home and he tells his
grandson, ‘This case is about whether a state can ignore U.S. treaty
obligations,’ we lose. So I spent a lot of time thinking about, What’s a
different narrative to explain this case?”
Eventually Cruz figured it out. Medellín v. Texas
would no longer be a fight between Texas and the United States; instead
it would be a fight between the White House and Congress. Before the
court, Cruz argued that if President Bush wanted to order Texas to
reopen the case, he would need the specific authorization of Congress;
without it, the president was violating the separation of powers. Six
justices concurred with Cruz — including one liberal, John Paul Stevens,
to the surprise of many observers. Cruz won the case.
Cruz
addresses the press outside the Supreme Court after defending the
redistricting of Texas in 2006. (Photo: Kevin Clark/The Washington
Post/Getty Images)
Cruz’s other standout Supreme Court performance wasn’t as high-profile as Medellín.
But according to Ho, Cruz still helped to shape the winning strategy
from behind the scenes. When a homeless Texan sought to have a 10
Commandments monument removed from the grounds of the Texas State
Capitol in Van Orden v. Perry, Cruz prepared a brief that made many of the usual conservative arguments
about why the monument in question did not violate the separation of
church and state. But at least one of Cruz’s arguments was novel: that
monuments like Texas’ are innately pluralistic because they aren’t
derecognizing one thing in order to recognize something else.
“This
is simply not a context in which the State is reasonably understood to
be taking sides,” Cruz wrote. “The many monuments commemorating veterans
do not communicate disapproval of pacifists; the Tribute to Children
does not reflect negatively on older Texans; the Hiker and horse-riding
Cowboy monuments send no message concerning motorized transport; and the
Volunteer Firemen monument reflects no official disapproval of those
who pursue firefighting as a paid profession.”
The
Court again sided with Cruz. In fact, the Texan’s argument, delivered
before the court by Abbott, was so convincing that it swayed even
Stephen Breyer, a liberal justice who simultaneously came to the
opposite conclusion in another, nearly identical 10 Commandments case.
“Ted
has this powerful combination,” Ho says. “He’s able to fight for his
vision of the Constitution and to fight for his principles. But he’s
able to do so with the kind of rhetoric and the style of argumentation
that convinces people who would normally disagree with him.”
Maybe
so. But while Cruz clearly holds strong, sincere views on the original
intent of the Framers and the power of free-market economics, winning —
the argument, the debate, the case, the election — seems to be at least
as important to him.
After
leaving the Texas attorney general’s office in 2008, for example, Cruz
joined the Houston office of the international law firm Morgan Lewis,
where as a partner he earned $1.2 million in 2009 and $1.7 million in
2010. Few of Cruz’s cases at Morgan Lewis had anything to do with
principle; some even appeared to contradict his oft-stated concern for
everyday Americans struggling to get ahead in a globalized,
too-big-to-fail economy. He served as counsel for drug manufacturer
Pfizer in a lawsuit brought by a group of public hospitals and community
health centers. He represented a student-loan company challenging the
dismissal of a bankrupt student’s debt. He did the same for an insurance
company attempting to avoid paying a plaintiff’s legal bills. And in
November 2010, when Chinese tire manufacturer Shandong Linglong appealed
a $26 million jury verdict awarded to a Florida businessman who alleged
that the company had been using stolen blueprints to duplicate his
designs, Cruz sided with the Chinese company over the American
entrepreneur.
“In
both public service and private practice, I was fortunate to enjoy
multiple litigation victories in cases where the outside world deemed
the odds all but insurmountable,” Cruz would later explain. “And I think the way to do so is to focus very pragmatically on how to win the case.”
That
is Cruz in a nutshell: principled about where he ultimately wants to
go, but pragmatic about how he gets there. How is he reframing the
debate? How is he using the rules to his advantage? At the end of the
day, Cruz has always been that restless 19-year-old up late in his dorm
room trying to calculate what he could “have done to get more points.”
And he probably always will be.
Editor's note: in this whole very long, very interesting article, they never mention once how much Ted loves Jesus. Could it be, gawd forbid, that he loves himself more?
And now from the University of New South Wales School of Physics in Sydney, Australia ...some shit scientists made up
Click here for the original article, complete with animations and links for further information.
The Foucault pendulum
The
Foucault pendulum: a simple explanation, some history
about the ideas of inertial frames, some
implications, correction of a few common misunderstandings and finally a
detailed analysis of the motion.
The
pendulum ball (above, left) has just been released from in front
of the camera position. The close-up (middle) shows a fine cable
under the handrail of the stairs. Behind this is a line on the
wall. Together they define a reference plane in the North-South
direction.
One
hour later, the amplitude of the swing has diminished, and the
plane has precessed about 9 degrees in the anti-clockwise direction
(Sydney is in the Southern hemisphere*). We clearly see the pendulum
crossing the reference plane.
Why Does The
Orbit Of Foucault's Pendulum Precess?
Suppose* someone
put a pendulum above the South Pole and sets it swinging in a simple arc.
To someone directly above the Pole and not turning with the earth, the
pendulum would seem to trace repeatedly an arc in the same plane while
the earth rotated slowly clockwise below it. To someone on the earth, however,
the earth seems to be stationary, and the plane of the pendulum's motion
would seem to move slowly anticlockwise, viewed from above. We say that
the pendulum's motion precesses. The earth turns on its axis every
23.93 hours, so to the terrestrial observer at the pole, the plane of the
pendulum seems to precess through 360 degrees in that time.
The
situation is more complicated for other latitudes. On the equator,
the pendulum would not precess at all - its precession period is infinite.
At intermediate latitudes the period has intermediate values. One can
calculate that the precession period for an ideal pendulum and support
system is 23.93 hours divided by the sine of the latitude (see details).
For example, at Sydney's latitude of 34 degrees S, the period is about
43 hours, a precession rate of about one degree every seven minutes.
The same
effect that causes a pendulum to appear to veer slightly to the left
(in the Southern hemisphere) is also responsible for the apparent motion
of the major ocean currents. In the Southern hemisphere these are anticlockwise
(they appear to turn to the left) and conversely in the Northern hemisphere.
One might
choose to say that the earth was stationary but that a mysterious force
makes moving objects turn. Using Newton's laws and the known rotation
rate of the earth, one can calculate the size of these "forces", which
are called Coriolis forces. Because it is so convenient to measure
motion with respect to the surface of the earth, these forces are often
used in calculation.
The animation
below shows a pendulum swinging above the South pole. At left is the
view from a position high above the equator at midday on the equinox---an
observer near the sun would see this. The view at right is the view
from directly below the South pole. Note how the path, as seen from
the Earth, curves always to the left. (To make the details easy to
see, the pendulum is depicted as very large and very slow. the amplitude
of its motion was chosen equal to the radius of the Earth, and its
period 8 hours: these values have no special significance. The animation
makes some approximations about the motion.
The acceleration due to the Earth's
rotation, at Sydney's latitude, is 28 mm.s−2. This requires a
force that is 0.3% of your weight, and it doesn't vary quickly. From
this calculation, you wouldn't expect to feel the Earth rotating. Due to
its orbit around the sun, the acceleration is 7 mm.s−2. The
speeds may be high, but the accelerations are trivial. In motion, you
don't feel speed, you feel the forces associated with acceleration. (See
Physclips' section on circular motion for the details of these calculations.)
The rotation
of the Earth does, however, account for the direction of the major circulations
of air and wind on the planet. A non-mathematical discussion of the coriolis
forces that give rise to these currents.
The 'plane' of the pendulum's swing is not fixed in space
It
is worthwhile correcting a common misunderstanding about Foucault's
Pendulum. It is sometimes said (perhaps poetically) that the pendulum swings in
a plane fixed with respect to the distant stars while the Earth rotates beneath it.
This is true at the poles. (It is also true for a pendulum swinging
East-West at the equator.) At all other latitudes, however, it is not true. At all other latitudes, the plane of the pendulum's motion rotates with respect to
an inertial frame.
It
is easy to deal with this misunderstanding. Consider a pendulum at the
equator, swinging in a North South plane. It's obvious from symmetry
that the plane of this pendulum doesn't rotate with respect to the earth
and that, relative to an inertial frame, it rotates once every 24
hours.
Alternatively,
consider the motion of a point on the earth at a place that is neither
at the poles or the equator. During a day, a vertical line at that place
traces out a cone, as shown in the sketch at right. (If the earth were
not turning, the half angle of the cone would be 90° minus the
latitude.) During each cycle of the pendulum, when it reaches its lowest
point its supporting wire passes very close to the vertical. So, at
each lowest point of the pendulum, its wire is a different line in this
cone. This cone is not a plane, so those lines do not all lie in the
same plane!
For
yet another argument, consider the motion of the pendulum after one
rotation of the earth. With respect to the earth, the period of
precession of the pendulum is 23.9 hours divided by the sine of the
latitude. For most latitudes, this is considerably longer than a day.
So, after the earth has turned once, the pendulum has not returned to
its original plane with respect to the earth. For example, our pendulum
in Sydney precesses at a rate of one degree every seven minutes, or one
complete circle in 43 hours.
(I
apologise for emphasising this rather obvious point. I only do so
because a correspondent has pointed out to me that many web pages about
the Foucault pendulum – and even, allegedly, a few old text books! –
make the mistake of stating that the pendulum swings in a fixed plane
while the earth rotates beneath it.)
So,
what is the path of motion of the pendulum? Remember that the point of
suspension of
the pendulum is accelerating around Earth's axis. So
the forces acting on the pendulum are a little complicated, and to
describe its motion requires some mathematics. (Indeed, even talking of a 'plane' of motion on a short time scale is an approximation because even in half a cycle the
supporting wire actually sweeps out a very slightly curved
surface.)
Our
Foucault Pendulum
The
Foucault Pendulum at the School of Physics of The University
of New South Wales is a "hands-on" version. There
is no electromagnetic drive but, because of its size once it
is started it will swing for several hours. Visitors are invited
to start it swinging in a plane that is accurately defined
by a fixed vertical wire and a vertical line on the wall. (See
the animation above) The pendulum takes seven minutes to
precess one degree, but even smaller angles than this can be
seen by sighting along the reference plane.
The
Motion of Foucault's Pendulum
For
more information about the motion of the Foucault pendulum
see: