Pendulum (drum and bass band) 2009-11: Immersion
Where did Pendulum originate?
Where did Pendulum originate?
Pendulum once again toured Europe in 2009. During this tour they announced that they were working on their third studio album, Immersion. It was announced in December 2009 that Pendulum would be touring for their new album in May 2010. The release date of the album was announced to be sometime "in May" during the live preview party at Matter, and was then announced to be released on 24 May. Pendulum previewed their album Immersion at the Ear Storm night at London's Matter nightclub on Friday 22 January. "Salt in the Wounds", a track from their new album, was Zane Lowe's Hottest Record in the World on BBC Radio 1 on 25 January 2010. On Zane Lowe's show, it was also announced that he wanted to join the band and the first single from the new album would be called "Watercolour". This single also received its first play on Zane Lowe's BBC Radio 1 show on 8 March 2010, and was his Single of the Week for that week. In December 2010, "Watercolour" was found to be featured in the soundtrack of the 2010 hit game "Need for Speed: Hot Pursuit". On 1 April, the music video for "Salt in the Wounds" was released. The video is unique in that it is, according to the band's website, "...the world's first 360deg interactive music video."  "Watercolour" claimed the No.4 spot in the UK Singles Chart, making it their biggest hit to date. On 21 May 2010, the band headlined the annual Radio 1's Big Weekend festival which was held at the Vaynol Estate, Bangor, Gwynedd. The second single from the album, "Witchcraft", was released on 18 July and charted at No.29 in the UK Singles chart, making it their third highest charted single in the UK. The third single from Immersion was "The Island", and just missed the UK Top 40 at No. 41.  Rob Swire had stated that if it had achieved greater success than "Witchcraft", he would have released a song entitled "Ransom", which was taken off Immersion before the album's release. Swire revealed the original files for "Ransom" were corrupted, and that he has no plans to recreate them, therefore it will not be released. However, on 6 April 2011, Pendulum released "Ransom" as a single via their website with all proceeds going to the Help for Japan fund after the tsunami. "Crush" was released as the fourth single in January 2011. In January 2011, Pendulum released a Deluxe Edition of Immersion via iTunes which contained the album's original 15 tracks and a collection of remixes of "Watercolour", "Witchcraft" and "The Island" by other artists including deadmau5, Tiesto and Chuckie. Both the UK and US store were also given the music videos of those three tracks in the release. CANNOTANSWER
CANNOTANSWER
A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.

Although the ballistic pendulum is considered obsolete, it remained in use for a significant length of time and led to great advances in the science of ballistics. The ballistic pendulum is still found in physics classrooms today, because of its simplicity and usefulness in demonstrating properties of momentum and energy. Unlike other methods of measuring the speed of a bullet, the basic calculations for a ballistic pendulum do not require any measurement of time, but rely only on measures of mass and distance.

In addition its primary uses of measuring the velocity of a projectile or the recoil of a gun, the ballistic pendulum can be used to measure any transfer of momentum. For example, a ballistic pendulum was used by physicist C. V. Boys to measure the elasticity of golf balls, and by physicist Peter Guthrie Tait to measure the effect that spin had on the distance a golf ball traveled.

History
 
The ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins (1707–1751), and published in his book New Principles of Gunnery, which revolutionized the science of ballistics, as it provided the first way to accurately measure the velocity of a bullet.

Robins used the ballistic pendulum to measure projectile velocity in two ways. The first was to attach the gun to the pendulum, and measure the recoil. Since the momentum of the gun is equal to the momentum of the ejecta, and since the projectile was (in those experiments) the large majority of the mass of the ejecta, the velocity of the bullet could be approximated. The second, and more accurate method, was to directly measure the bullet momentum by firing it into the pendulum. Robins experimented with musket balls of around one ounce in mass (28 g), while other contemporaries used his methods with cannon shot of one to three pounds (0.5 to 1.4 kg).

Robins' original work used a heavy iron pendulum, faced with wood, to catch the bullet.  Modern reproductions, used as demonstrations in physics classes, generally use a heavy weight suspended by a very fine, lightweight arm, and ignore the mass of the pendulum's arm. Robins' heavy iron pendulum did not allow this, and Robins' mathematical approach was slightly more complex. He used the period of oscillation and mass of the pendulum (both measured with the bullet included) to calculate the rotational inertia of the pendulum, which was then used in the calculations. Robins also used a length of ribbon, loosely gripped in a clamp, to measure the travel of the pendulum. The pendulum would draw out a length of ribbon equal to the chord of pendulum's travel.

The first system to supplant ballistic pendulums with direct measures of projectile speed was invented in 1808, during the Napoleonic Wars and used a rapidly rotating shaft of known speed with two paper disks on it; the bullet was fired through the disks, parallel to the shaft, and the angular difference in the points of impact provided an elapsed time over the distance between the disks. A direct electromechanical clockwork measure appeared in 1848, with a spring-driven clock started and stopped by electromagnets, whose current was interrupted by the bullet passing through two meshes of fine wires, again providing the time to traverse the given distance.

Mathematical derivations
Most physics textbooks provide a simplified method of calculation of the bullet's velocity that uses the mass of the bullet and pendulum and the height of the pendulum's travel to calculate the amount of energy and momentum in the pendulum and bullet system. Robins' calculations were significantly more involved, and used a measure of the period of oscillation to determine the rotational inertia of the system.

Simple derivation
We begin with the motion of the bullet-pendulum system from the instant the pendulum is struck by the bullet.

Given , the acceleration due to gravity, and , the final height of the pendulum, it is possible to calculate the initial velocity of the bullet-pendulum system using conservation of mechanical energy (kinetic energy + potential energy).  Let this initial velocity be denoted by . Suppose the masses of the bullet and pendulum are  and  respectively.

The initial kinetic energy of the system 

Taking the initial height of the pendulum as the potential energy reference , the final potential energy when the bullet-pendulum system comes to a stop  is given by 

So, by the conservation of mechanical energy, we have:

Solve for velocity to obtain:  

We can now use momentum conservation for the bullet-pendulum system to get the speed of the bullet, , before it struck the pendulum. Equating the momentum of the bullet before it is fired to that of the bullet-pendulum system as soon as the bullet strikes the pendulum (and using  from above), we get:

Solving for :

Robins' formula
Robins' original book had some omitted assumptions in the formula; for example, it did not include a correction to account for a bullet impact that did not match the center of mass of the pendulum. An updated formula, with this omission corrected, was published in the Philosophical Transactions of the Royal Society the following year. Swiss mathematician Leonhard Euler, unaware of this correction, independently corrected this omission in his annotated German translation of the book. The corrected formula, appearing in a 1786 edition of the book, was:

where:
  is the velocity of the ball in units per second
  is the mass of the ball
  is the mass of the pendulum
  is the distance from pivot to the center of gravity
  is the distance from pivot to the point of the ball's impact
  is the chord, as measured by the ribbon described in Robins' apparatus
  is the radius, or distance from the pivot the attachment of the ribbon
  is the number of oscillations made by the pendulum in one minute

Robins used feet for length and ounces for mass, though other units, such as inches or pounds, may be substituted as long as consistency is maintained.

Poisson's formula
A rotational inertia based formula similar to Robins' was derived by French mathematician Siméon Denis Poisson and published in The Mécanique Physique, for measuring the bullet velocity by using the recoil of the gun:

where:
  is the mass of the bullet
  is the velocity of the bullet
  is the distance from pivot to the ribbon
  is the distance from bore axis to pivot point
  is the combined mass of gun and pendulum
  is the chord measured by the ribbon
  is the radius from pivot to the center of mass of gun and pendulum (measured by oscillation, as per Robins)
  is gravitational acceleration
  is the distance from the center of mass of the pendulum to the pivot

 can be calculated with the equation:

Where  is half the period of oscillation.

Ackley's ballistic pendulum
P.O. Ackley described how to construct and use a ballistic pendulum in 1962. Ackley's pendulum used a parallelogram linkage, with a standardized size that allowed a simplified means of calculating the velocity.

Ackley's pendulum used pendulum arms of exactly 66.25 inches (168.3 cm) in length, from bearing surface to bearing surface, and used turnbuckles located in the middle of the arms to provide a means of setting the arm length precisely.  Ackley recommends masses for the body of the pendulum for various calibers as well; 50 pounds (22.7 kg) for rimfire up through the .22 Hornet, 90 pounds (40.9 kg) for .222 Remington through .35 Whelen, and 150 pounds (68.2 kg) for magnum rifle calibers.  The pendulum is made of heavy metal pipe, welded shut at one end, and packed with paper and sand to stop the bullet.  The open end of the pendulum was covered in a sheet of rubber, to allow the bullet to enter and prevent material from leaking out.

To use the pendulum, it is set up with a device to measure the horizontal distance of the pendulum swing, such as a light rod that would be pushed backwards by the rear of the pendulum as it moved.  The shooter is seated at least 15 feet (5 m) back from the pendulum (reducing the effects of muzzle blast on the pendulum) and a bullet is fired into the pendulum.  To calculate the velocity of the bullet given the horizontal swing, the following formula is used:

where:
  is the velocity of the bullet, in feet per second
  is the mass of the pendulum, in grains
  is the mass of the bullet, in grains
  is the horizontal travel of the pendulum, in inches

For more accurate calculations, a number of changes are made, both to the construction and the use of the pendulum.  The construction changes involve the addition of a small box on top of the pendulum.  Before weighing the pendulum, the box is filled with a number of bullets of the type being measured.  For each shot made, a bullet can be removed from the box, thus keeping the mass of the pendulum constant.  The measurement change involves measuring the period of the pendulum.  The pendulum is swung, and the number of complete oscillations is measured over a long period of time, five to ten minutes.  The time is divided by the number of oscillations to obtain the period.  Once this is done, the formula  generates a more precise constant to replace the value 0.2018 in the above equation.  Just like above, the velocity of the bullet is calculated using the formula:

References

Bibliography
 Benjamin Robins, James Wilson, Charles Hutton (1805). New Principles of Gunnery. F. Wingrave.
 "Ballistic pendulum". Encyclopædia Britannica

External links
Ballistic pendulum calculator
Ballistic Pendulum demonstrated by Walter Lewin

Pendulums
Ballistics Psyclone is a  ride at Canada's Wonderland. On May 5, 2002, this Mondial ride was opened to the public at the park. The 1 minute and 54 second ride features 40 seats facing outwards which rotate from a central pendulum as the ride reaches its maximum arc angle of 120 degrees. Even though the ride height is , when the ride reaches the top of its swing, the height becomes  high.

Ride experience
The rider's experience depends on where they are seated on the ride. Before the ride begins, the floor under the riders' feet descends lower (almost like going deeper in the ground) due to how the pendulum swings. If the floor did not move, serious injury to riders' legs and bodies would occur. Due to the way in which the seats rotate, all riders face different angles of the ride. Depending on where the rider is seated, they may experience some air-time as the swing reaches its maximum angle. When the ride cycle ends, the pendulum returns to the 'loading position' and the floor rises to the riders' feet, allowing riders to exit and enter the ride.

Structure
Psyclone is made primarily out of 7 major parts: the 4 supports around the ride which support the motor that allows the pendulum to swing, the motor itself (the blue part on top of the ride) which supports the pendulum, the pendulum itself which supports the seats for the ride, and the seats themselves.

References

External links

 Official Psyclone page

Pendulum rides
Canada's Wonderland
Amusement rides manufactured by Mondial
Amusement rides introduced in 2002
Cedar Fair attractions
2002 establishments in Canada A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity.

Pendulum may also refer to:

Devices
 Pendulum (mathematics), the mathematical principles of a pendulum
 Pendulum clock, a kind of clock that uses a pendulum to keep time
 Pendulum car, an experimental tilting train
 Foucault pendulum, a pendulum that demonstrates the Earth's rotation
 Spherical pendulum
 Spring pendulum
 Conical pendulum
 Centrifugal pendulum absorber, torsional vibration reduction by using a pendulum principle
 For other types and uses of pendulums, see: :Category:Pendulums
 Mackerras Pendulum, a model devised by Malcolm Mackerras to predict election outcomes
 Pendulum (torture device), a device allegedly used by the Spanish Inquisition
 Pendulum Instruments, a Swedish manufacturer of scientific instruments

Music
 Pendulum (Australian band), an Australian electronic rock group formed in 2002
 Pendulum (ambient band), an Australian house music group formed in 1994

Albums
 Pendulum (Broadcast EP), and its title track
 Pendulum (Creedence Clearwater Revival album)
 Pendulum (Dave Liebman album), and its title track
 Pendulum (Eberhard Weber album), and its title track
 Pendulum (Tara Simmons EP), and its title track
 The Pendulum, a comic book miniseries based on Insane Clown Posse's Dark Carnival universe, and associated songs and album

Songs
 "Pendulum" (song), by FKA Twigs
 "Pendulum", by Katy Perry from the album Witness
 "Pendulums", by Sarah Harmer from the album All of Our Names

 "Penduli Pendulum", by Bobbie Gentry from The Delta Sweete
 "The Pendulum Song", song written by Al Hoffman and John Murray
 Pendulum Music, a composition by Steve Reich involving microphones swinging above speakers like pendulums

Books and periodicals 
Pendulum, by John Christopher, 1968 
The Pendulum, by Annie S. Swan, 1972 
Pendulum, by A. E. Van Vogt, 1978
Pendulum, by Adam Hamdy, 2017
The Pendulum, a student newspaper at Elon University
The Pendulum, a publication devoted to radiesthesia

Film
Pendulum (film), a 1969 film starring George Peppard
Pendulum, a 2001 film starring Rachel Hunter and James Russo

Other
 Pendulum, a trade name for the preemergent herbicide pendimethalin
 Pendulum, several types of Digimon virtual pets

See also