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Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion. The fixed axis hypothesis excludes the possibility of an axis changing its orientation, cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will appear; this article assumes that the rotation is stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; the expressions for the kinetic energy of the object, for the forces on the parts of the object, are simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is taught in introductory physics courses after students have mastered linear motion.

A rigid body is an object of finite extent in which all the distances between the component particles are constant. No rigid body exists. For our purposes a rigid body is a solid which requires large forces to deform it appreciably. A change in the position of a particle in three-dimensional space can be specified by three coordinates. A change in the position of a rigid body is more complicated to describe, it can be regarded as a combination of two distinct types of motion: translational motion and circular motion. Purely translational motion occurs when every particle of the body has the same instantaneous velocity as every other particle. Under translational motion, the change in the position of a rigid body is specified by three coordinates such as x, y, z giving the displacement of any point, such as the center of mass, fixed to the rigid body. Purely rotational motion occurs; this line is called the axis of rotation. The radius vectors from the axis to all particles undergo the same angular displacement at the same time.

The axis of rotation need not go through the body. In general, any rotation can be specified by the three angular displacements with respect to the rectangular-coordinate axes x, y, z. Any change in the position of the rigid body is thus described by three translational and three rotational coordinates. Any displacement of a rigid body may be arrived at by first subjecting the body to a displacement followed by a rotation, or conversely, to a rotation followed by a displacement. We know that for any collection of particles—whether at rest with respect to one another, as in a rigid body, or in relative motion, like the exploding fragments of a shell, the acceleration of the center of mass is given by F n e t = M a c m where M is the total mass of the system and acm is the acceleration of the center of mass. There remains the matter of describing the rotation of the body about the center of mass and relating it to the external forces acting on the body; the kinematics and dynamics of rotational motion around a single axis resemble the kinematics and dynamics of translational motion.

A particle moves in a circle of radius r. Having moved an arc length s, its angular position is θ relative to its original position, where θ = s r. In mathematics and physics it is conventional to use the natural unit radians rather than degrees or revolutions. Units are converted as follows: 1 revolution = 360 ∘ = 2 π radians, 1 rad = 180 ∘ π ≈ 57.27 ∘. An angular displacement is a change in angular position: Δ θ = θ 2 − θ 1, where Δ θ is the angular displacement, θ 1 is the initial angular position and θ 2 is the final angular position. Change in angular displacement per unit time is called angular velocity with direction along the axis of rotation; the symbol for angular velocity is ω and the units are rad s−1. Angular speed is the magnitude of angular velocity. Ω ¯ =

The Yappar River is a river located in the Gulf Country region of Far North Queensland, Australia. The river rises below the Gregory Range near Esmeralda in an area of ephemeral watercourses and stony sandstone ridges vegetated with Eucalyptus miniata and spinifex on the ridge tops. Further down from the ridges areas of paperbark are found; the river flows in a north-westerly direction through Esmeralda Station and savannah county parallel with the Clara River, through the channel country until it reaches Yappar Station where it reaches its confluence with the Norman River at the western boundary of Claraville. The Yappar has seven minor tributaries from source to mouth and descends 374 metres over its 340 kilometres course. List of rivers of Queensland

Steve Harvey is a syndicated daytime talk show that ran for five seasons from September 4, 2012, to July 13, 2017, with a total of 920 episodes during its run. It was hosted by comedian and media personality Steve Harvey and taped at the NBC Tower studios in Chicago, Illinois; the show was produced by Endemol Shine North America and distributed by NBCUniversal Television Distribution. On November 11, 2016, it was announced that Steve Harvey would be cancelled at the conclusion of the 2016–17 season. Concurrently, it was announced that Harvey would host a new talk show beginning the following season, produced in Los Angeles in partnership with IMG and NBCUniversal Television Distribution. Out of the five new talk shows to premiere during the 2012–13 television season, Steve Harvey ranked second, behind Katie, but ahead of The Jeff Probst Show, The Ricki Lake Show, The Trisha Goddard Show. During the week of December 31, 2012, Steve Harvey averaged 1.987 million viewers. Steve Harvey on IMDb Official website

Auzet is a French commune in the Alpes-de-Haute-Provence department in the Provence-Alpes-Côte d'Azur region of south-eastern France. The inhabitants of the commune are known as Auzetanes. Auzet is located some 45 km north-east of 35 km west by south-west of Barcelonnette. Access to the commune is by the D7 road from Seyne in the north which passes through the length of the commune and the village and joins the D900A on the southern border of the commune. Apart from the village there are the hamlets of L'Infernet, L'Infernet Haut, L'Infernet Bas north of the village; the commune is rugged with snow-capped mountains and forested slopes with 1,168 hectares of forest. Numerous streams rise in the north of the commune and flow south: the Grave river rises in the north of the commune and gathers countless tributaries as it flows south to join the Bés on the southern border; the area of the commune is 3,453 hectares and its altitude varies between 1,068 and 2,028 metres. The village is located at 1,180 m above sea level.

The highest peaks are Clot de Bouc and the cols of Fanget and Grangeasse. None of the 200 communes in the department is in a no seismic risk zone; the Canton of Seyne to which Auzet belongs is zone 1b according to the deterministic classification of 1991, based on the historical seismic activities, zone 4 according to the probabilistic classification EC8 of 2011. Auzet is exposed to four other natural hazards: avalanche wildfire flood landslideAuzet is not exposed to any risk of technological origin identified by the prefecture. No risk prevention plan for foreseeable natural risks exists for the commune and there is no DICRIM. In 2013 the commune built two certified passive buildings with four housing units at 1200 m altitude; the passive concept is the most advanced in the world and is the only one which can dispense with conventional heating. The heating power is provided by 10w/m2 of fresh air; the name Auzet appears for the first time in charters of 1058 under the name Ausitum. In referring to sheep belonging to the Abbey of Saint Victor, Marseille, it appeared as Alisino in 814 with forty inhabitants.

In 1958 loggers discovered a deposit of iron and bronze objects dating from the La Tène period: spearheads and bits for horses. In 1351 reference was made to the community, or rather to its chaplain, indicating that the priest of the church did not depend on an Abbey. From the 13th to the 18th century there was a mill in the ravine of Saint Andrieu; the death of Queen Joanna I re-opened a succession crisis at the head of the County of Provence with the cities of the Aix Union supporting Charles de Duras against Louis I of Anjou. The Auzet community supported Duras until 1386 switched sides to join the Angevins through patient negotiation by Marie of Blois, widow of Louis I and regent for their son Louis II. In the 18th century a fair was held in Auzet. During the French Revolution the commune had a patriotic society formed after the end of 1792. In the 19th century Auzet was one of the last towns in the region to develop a school: in the survey of 1863 it was among the 17 communes in the department not to possess one and awaited the Jules Ferry laws to install it.

During the Second World War a colony of Jewish children at the Col du Fanget was saved. Joseph Isoard and his brother Armand with their wives Julie and Simone saved Jews from deportation and were therefore distinguished as Righteous among the Nations. List of Successive Mayors; the evolution of the number of inhabitants is known from the population censuses conducted in the commune since 1793. From the 21st century, a census of communes with fewer than 10,000 inhabitants is held every five years, unlike larger communes that have a sample survey every year. In 2009 the active population stood at 43 people including 7 unemployed; these workers are employed and work outside the commune. Most of the employees in the commune have jobs in services and administration with 14 positions. At 1 January 2011 businesses active in the commune were divided between farms and the tertiary sector. At the end of 2010 the primary sector had eight businesses; the number of farms, according to the Agreste survey by the Ministry of Agriculture, was 7 in 2010, all livestock.

Auzet had suffered a severe loss of farms, losing six of the ten farms present in the commune from 1988 to 2000. The utilized agricultural area has increased from 418 hectares in 1988 to 728 hectares in 2010 distributed among cattle and sheep. Auzet is included in the area of the label Apples of Alpes de Haute-Durance. At the end of 2010 the secondary sector had four businesses employing two people. At the end of 2010 the tertiary sector had eight businesses plus two institutions in the administrative sector and social; the main employer is a school of music - the Music and Environment Centre Fontaine de l’Ours created in 1997. According to the Departmental Observatory of tourism, tourism is important for the commune with more than five tourist arrivals per capita. Most

Lesbian, gay and transgender persons in Libya face legal challenges not experienced by non-LGBT residents. Since the fall of Gaddafi regime in 2011, the status regarding homosexuality in Libya remains unchanged; the country's criminal code prohibits all sexual activity outside of a lawful marriage. Under Article 410 of the Libyan Penal Code, Private homosexual acts between consenting adults are illegal. In the 1990s, Libyan leader Muammar Gaddafi began to enact "purification" laws designed to enforce a harsh view of Islamic law on the population. Libyan courts were given the power to use amputation and other punishments against persons found to be violating traditional Islamic morality. In 2010, the Gay Middle East blog, reported that two adult men had been charged with "indecent acts", which meant cross-dressing and homosexual conduct. Female homosexuality would appear to be illegal, as is making any sort of public acknowledgment that a person is gay. In 2010 a French asylum case involved a Libyan girl who sought asylum after being jailed and returned to her family for a forced marriage after she made a public statement online that she was gay.

Vigilante executions, in lieu of the penal code, are more commonplace in ISIS-controlled territories. The criminal code is still technically in operation, although much of Libya is run by competing militias who may choose to execute LGBT people. ISIS in Libya has publicly executed men for homosexuality; the Gaddafi government did not permit the public advocacy of LGBT rights. When discussed, it was always in keeping with traditional Islamic morality. In 2003, Gaddafi stated that he believed that it was "impossible" to contract AIDS–HIV through unprotected, heterosexual vaginal sex; the Transitional post-Gaddafi government continues to oppose LGBT rights. In February 2012 a Libyan delegate sparked outrage after telling a United Nations human rights panel that gay people threaten the future of the human race; the Transitional Constitution stipulates that Islam is a source of law. The Transitional Constitution pledges to respect the people's right to have a private life.2019: As of 2019, Libya has one LGBTQ+ NGO called Kun Libya.

Libya's LGBT identifying population remains as of today under pressure to remain closeted due to the fall of the state since 2011. Human rights in Libya LGBT rights in Africa

Jai Gangaajal is a 2016 Indian crime drama film directed by Prakash Jha. It is a follow-up to the 2003 crime film Gangaajal, stars Priyanka Chopra in the lead role with Jha appearing in a supporting role, it features Manav Kaul, Rahul Bhat, Queen Harish. The film was released worldwide on 4 March 2016; the Government of Madhya Pradesh declared Jai Gangaajal tax-free on 9 March 2016 and was a moderate box office success. Babloo Pandey, the MLA of Bankipur district and his brother Dabloo Pandey run a jungle raaj in their town of Lakhisarai, they are grabbing land for a power plant. The home minister, Ramakant Chowdhary appoints Abha Mathur, IPS as the SP expecting her to be soft towards the criminals and supportive to him, being her mentor as well as the home minister, but she goes all out against the criminal brothers. Her subordinates get encouraged by her brave acts against corruption and bringing the jungle raaj to an end. Bhola Nath Singh aka B. N. Singh is a corrupt circle Officer who has helped the brothers for a long time by using legal loopholes and other corrupt ways to keep them out of harm's way in return for financial favours and political support.

As the brothers feel cornered, Dabloo's goons kidnaps an orphaned teenage girl Sunita and her younger brother Nagesh refuse to give away the land. After the kidnapping, Dabloo rapes and kills the girl and hangs her from a tree showing this as a suicide just as her father had committed suicide too under pressure of selling the land. Singh comes to his senses after seeing this brutal crime and tries to arrest Dabloo Pandey, which starts a riot in the town inducing Nagesh, the younger brother of the murdered girl to use his belt throttle Dabloo's neck and killing him, seeing which the villagers gather around some more goons and the corrupt Sarpanch and kill them and hang them on the tree claiming it to be suicides; this starts a chain reaction where corrupt people are killed in similar manner elsewhere. Abha is unable to control these illegal killings, she tries her best to control the order. Singh gets injured. Babloo frantically searches for Nagesh, who has killed Dabloo and is now hidden away by Singh from Babloo.

Babloo's goons locate Nagesh and take him in a gunny bag to Babloo, who wants to eliminate him by hanging. But in a final showdown, Babloo Pandey gets arrested and the reign of corruption and anarchy comes to an end. Priyanka Chopra as SP Abha Mathur, IPS Prakash Jha as DSP Bhola Nath Singh aka B. N. Singh. Kiran Karmarkar as Ramakant Chowdhary, Home Minister Manav Kaul as MLA Babloo Pandey Ninad Kamat as Dabloo Pandey Murali Sharma as Munna Mardani Pranay Narayan as Ratnakar Rahul Bhat as Pawan Raghav Vega Tamotia as Sunita Ayush Mahesh Khedekar as Nagesh, Sunita's brother Jagat Singh Solanki as Amreek Tiwari Indraneel Bhattacharya as IG Mithilesh Kumar IPS Ritesh M M Shukla as Factory Man Jai Gangaajal was shot in Bhopal. Priyanka Chopra started shooting for the film in June 2015; the shooting took place in places like Jama Masjid Chowk bazaar in old Bhopal. Music for this film is given by Salim–Sulaiman, while the lyrics have been penned by Manoj Muntashir. Prakash Jha has written additional lyrics for the song "Najar Tori Raja".

Jai Gangaajal got mixed reviews from the critics. Bollywood Hungama gave 3 stars out of 5, mentioning the screenplay engaging, cinematography decent, editing praiseworthy, dialogues excellent; as for the performances, Priyanka Chopra delivers a superlative performance, be it her perfect and impeccable timing or her intimidating screen persona and presence but Prakash Jha pushes himself a bit too hard to get the nuances and the finer points of his character. Rajeev Masand gave the film 2.5 stars out of 5, mentioning it as a predictable police drama filled with the usual stereotypes but added that Priyanka Chopra and Prakash Jha's performances engaging. Srijana Mitra Das from The Times of India gave the film 3.5 stars. She praised the dialogues and story, writing,"It weaves together crucial contemporary threads – land mafias, corrupt netas, broker-cops, broken farmers-with Jha's enduring concern about vigilante justice." She applauded Priyanka Chopra's performance, writing, "Priyanka Chopra shines as'Madam Sir' Abha Mathur, whose lightning slaps and lathi charges have you applauding.

This is a polished, restrained Priyanka, who smiles but conveys the ethics and empathy of the law." She commended Rahul Bhat's cameo and the dynamics between BN and Dablu but was disappointed with Manav Kaul's performance in particular. Rohit Vats of Hindustan Times gave 2.5 stars, writing, "Jai Gangaajal is just another attempt at making a blockbuster, but it lacks the depth of Gangaajal and Apharan. Still, there's enough for the audience to keep whistling and clapping." According to him, Prakash Jha is restrained in dialogue delivery and effective in emotional scenes. He wrote that the storyline doesn't offer anything that haven't seen before but it has tear-inducing moments with explosive dialogues. Writing for NDTV, Saibal Chatterjee gave 2.5 stars, saying, "Despite the topical themes it tackles and all the supercharged action that unfolds on the screen, Jai Gangaajal never kicks into top gear." Shubhra Gupta from The Indian Express gave only 1.5 stars, writing "Priyanka Chopra's too-sophisticated unmade-up-make-up is distracting in her few convincing moments.

And the film goes on for far too long when we know how of it all will end." However, she was all praise for Prakash Jha's full-fledged role. Jai Gangaajal on IMDb Jai Gangaajal at Bollywood Hunga