- published: 02 Apr 2015
- views: 34870
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero or the point where if a force is applied causes it to move in direction of force without rotation. The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. All forces are equal and opposite. Calculations in mechanics are often simplified when formulated with respect to the center of mass.
In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.
The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.
In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.
In physics, mass is a property of a physical body. It is generally a measure of an object's resistance to changing its state of motion when a force is applied. It is determined by the strength of its mutual gravitational attraction to other bodies, its resistance to being accelerated by a force, and in the theory of relativity gives the mass–energy content of a system. The SI unit of mass is the kilogram (kg).
Mass is not the same as weight, even though we often calculate an object's mass by measuring its weight with a spring scale instead of comparing it to known masses. An object on the Moon would weigh less than it would on Earth because of the lower gravity, but it would still have the same mass.
For everyday objects and energies well-described by Newtonian physics, mass describes the amount of matter in an object. However, at very high speeds or for subatomic particles, special relativity shows that energy is an additional source of mass. Thus, any stationary body having mass has an equivalent amount of energy, and all forms of energy resist acceleration by a force and have gravitational attraction.
Center or centre may refer to:
Center of Mass
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Center of Mass
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An athlete uses physics to shatter world records - Asaf Bar-Yosef
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Simbucket Simulation - http://www.simbucket.com/simulation/center-of-mass-builder/ 095 - Center of Mass In this video Paul Andersen explains how the center of mass of an object represents the average position of matter in an object. The center of mass of a system is a combination of all the objects within the system. As long as no external torque is applied to the system the center of mass will be conserved. Do you speak another language? Help me translate my videos: http://www.bozemanscience.com/translations/ Music Attribution Title: String Theory Artist: Herman Jolly http://sunsetvalley.bandcamp.com/track/string-theory All of the images are licensed under creative commons and public domain licensing: DarKobra. Tango Tirestone Tire Icon., May 19, 2009. http://darkobra.deviantart.c...
In this video, David solves an example elastic collision problem to find the final velocities using the easier/shortcut approach. Watch the next lesson: https://www.khanacademy.org/science/physics/torque-angular-momentum/rotational-kinematics/v/angular-motion-variables?utm_source=YT&utm;_medium=Desc&utm;_campaign=physics Missed the previous lesson? https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/v/deriving-the-shortcut-to-solve-elastic-collision-problems?utm_source=YT&utm;_medium=Desc&utm;_campaign=physics Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different p...
How to find it, what it means, and some examples
GCSE Science Doodle Science teaches you high school physics in a less boring way in almost no time! Follow me: https://twitter.com/DoodleSci You can support me at: https://patreon.com/doodlescience Script: The centre of mass of an object is the point where the entire weight of an object appears to act. Working out the centre of mass of a symmetrical object is easy; it’s simply the point where the lines of symmetry cross. However it’s very unlikely that you’ll be dealing with such perfect shapes so you work it out by suspending the object freely, along with a plumb line. The centre of mass is always below the point of suspension, so by marking the vertical along the plumb line you know the centre of mass is somewhere along that line. By suspending the object from another point and rep...
View full lesson: http://ed.ted.com/lessons/an-athlete-uses-physics-to-shatter-world-records-asaf-bar-yosef When Dick Fosbury couldn't compete against the skilled high jumpers at his college, he tried jumping in a different way -- backwards. Fosbury improved his record immediately and continued to amaze the world with his new technique all the way to Olympic gold. Asaf Bar-Yosef explains the physics behind the success of the now dominant Fosbury Flop. Lesson by Asaf Bar-Yosef, animation by NEIGHBOR.
Finding the center of mass of an object
The Breaking pole paradox is not really a paradox but I didn't name it. This demonstration starts with a long thin wooden pole supported at either end atop two water glasses. A swift impulsive blow breaks the pole at it's center without managing to knock over the cups and spill a single drop. How is it possible? I am breaking it against the inertia of the pole, Swinging the metal bar as fast as I can with a quick hit would cause a quick downward acceleration on the wooden pole. But, since the wooden pole has a certain amount of inertia, it can't withstand the sudden acceleration force and so instead of being moved downward it simply breaks. As the pole breaks, the downward force is now acting as a torque, which now causes the two smaller pieces to rotate around their new respecti...
Lowerground Intro Animation. A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star. www.lowerground.com Audio by Michael Fakesch www.michaelfakesch.com
Playing with Dave Christenson's "DIVER" http://vimeo.com/746969 My first time using keyframes in After Effects, there's a lot of choppiness and misplaced anchor points (it's surprisingly difficult finding the center of mass on the divers). Update: Oh, "Graph Editor". That's pretty neat. It evens the end out a bit.
The system combines inertial and active camera stabilization. Inertial stabilization is based on matching the center of mass and the rotation axis. An air engine is used for rotation and active camera stabilization. The air engine counterbalances the forces causing unwanted camera tilt.
Music: Minz (http://minzmusic.net/) Video: June74 (http://www.fabriziopoce.com/) Laying down tracks just before the train passes. Sound-reactive, real time done using self-developed software (V-Module, a Max for Live // Ableton Live sketching and improvisation environment: fabriziopoce.com/max.html). Real time. 3D sculptures created by patterns of 144 cubes, modulated by frequency analysis of the incoming sound (144 bands). Patters are regenerated when camera moves beyond their center of mass and this by randomly crossing a few simple mathematical functions, creating newer patterns and variations. Cheers Fabrizio
This animation shows the unique triple-star system with a superdense neutron star and two white dwarf stars. The neutron star is a pulsar, emitting lighthouse-like beams of radiation as it spins on its axis. These beams, in blue, are seen sweeping through space as the neutron star rotates. At the start, you see this pulsar and its close companion white dwarf in orbit around their common center of mass. The animation zooms outward, showing this pair also in orbit with a more-distant, cooler white dwarf, and illustrates the motions of these three bodies. The entire system would fit within Earth's orbit around the Sun.
This clip seeks to explain the apparent paradox of skiers appearing "in the back seat" in the transition, based on a visualization of playing catch with a heavy "medicine ball," then recognizing that skiing is analogous to our skis playing catch with our center of mass in exactly the same way.
The first test of a cable-mounted camera rig that I designed and built in one day. The main part of the rig is a three degree of freedom wooden framework, which is held in place using butterfly nuts. Two pulleys (which are actually second-hand door runners) are attached to the top cross-piece of this wooden framework. The whole thing hangs off a piece of tensioned stranded steel cable, using a pair of carabiners clipped over the cable to secure the camera safely in the event of the pulleys running off the cable. The design is such that the camera's center of mass hangs vertically beneath the cable, no matter what orientation it has. The camera is a Canon XH-A1. Total cost of the rig (including the steel cable): AU$110. Two main problems exist with this rig: vibration and sway. The vibrat...
Simbucket Simulation - http://www.simbucket.com/simulation/center-of-mass-builder/ 095 - Center of Mass In this video Paul Andersen explains how the center of mass of an object represents the average position of matter in an object. The center of mass of a system is a combination of all the objects within the system. As long as no external torque is applied to the system the center of mass will be conserved. Do you speak another language? Help me translate my videos: http://www.bozemanscience.com/translations/ Music Attribution Title: String Theory Artist: Herman Jolly http://sunsetvalley.bandcamp.com/track/string-theory All of the images are licensed under creative commons and public domain licensing: DarKobra. Tango Tirestone Tire Icon., May 19, 2009. http://darkobra.deviantart.c...
In this video, David solves an example elastic collision problem to find the final velocities using the easier/shortcut approach. Watch the next lesson: https://www.khanacademy.org/science/physics/torque-angular-momentum/rotational-kinematics/v/angular-motion-variables?utm_source=YT&utm;_medium=Desc&utm;_campaign=physics Missed the previous lesson? https://www.khanacademy.org/science/physics/linear-momentum/elastic-and-inelastic-collisions/v/deriving-the-shortcut-to-solve-elastic-collision-problems?utm_source=YT&utm;_medium=Desc&utm;_campaign=physics Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different p...
How to find it, what it means, and some examples
GCSE Science Doodle Science teaches you high school physics in a less boring way in almost no time! Follow me: https://twitter.com/DoodleSci You can support me at: https://patreon.com/doodlescience Script: The centre of mass of an object is the point where the entire weight of an object appears to act. Working out the centre of mass of a symmetrical object is easy; it’s simply the point where the lines of symmetry cross. However it’s very unlikely that you’ll be dealing with such perfect shapes so you work it out by suspending the object freely, along with a plumb line. The centre of mass is always below the point of suspension, so by marking the vertical along the plumb line you know the centre of mass is somewhere along that line. By suspending the object from another point and rep...
View full lesson: http://ed.ted.com/lessons/an-athlete-uses-physics-to-shatter-world-records-asaf-bar-yosef When Dick Fosbury couldn't compete against the skilled high jumpers at his college, he tried jumping in a different way -- backwards. Fosbury improved his record immediately and continued to amaze the world with his new technique all the way to Olympic gold. Asaf Bar-Yosef explains the physics behind the success of the now dominant Fosbury Flop. Lesson by Asaf Bar-Yosef, animation by NEIGHBOR.
Finding the center of mass of an object
The Breaking pole paradox is not really a paradox but I didn't name it. This demonstration starts with a long thin wooden pole supported at either end atop two water glasses. A swift impulsive blow breaks the pole at it's center without managing to knock over the cups and spill a single drop. How is it possible? I am breaking it against the inertia of the pole, Swinging the metal bar as fast as I can with a quick hit would cause a quick downward acceleration on the wooden pole. But, since the wooden pole has a certain amount of inertia, it can't withstand the sudden acceleration force and so instead of being moved downward it simply breaks. As the pole breaks, the downward force is now acting as a torque, which now causes the two smaller pieces to rotate around their new respecti...
Lowerground Intro Animation. A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star. www.lowerground.com Audio by Michael Fakesch www.michaelfakesch.com
Playing with Dave Christenson's "DIVER" http://vimeo.com/746969 My first time using keyframes in After Effects, there's a lot of choppiness and misplaced anchor points (it's surprisingly difficult finding the center of mass on the divers). Update: Oh, "Graph Editor". That's pretty neat. It evens the end out a bit.
The system combines inertial and active camera stabilization. Inertial stabilization is based on matching the center of mass and the rotation axis. An air engine is used for rotation and active camera stabilization. The air engine counterbalances the forces causing unwanted camera tilt.
Music: Minz (http://minzmusic.net/) Video: June74 (http://www.fabriziopoce.com/) Laying down tracks just before the train passes. Sound-reactive, real time done using self-developed software (V-Module, a Max for Live // Ableton Live sketching and improvisation environment: fabriziopoce.com/max.html). Real time. 3D sculptures created by patterns of 144 cubes, modulated by frequency analysis of the incoming sound (144 bands). Patters are regenerated when camera moves beyond their center of mass and this by randomly crossing a few simple mathematical functions, creating newer patterns and variations. Cheers Fabrizio
This animation shows the unique triple-star system with a superdense neutron star and two white dwarf stars. The neutron star is a pulsar, emitting lighthouse-like beams of radiation as it spins on its axis. These beams, in blue, are seen sweeping through space as the neutron star rotates. At the start, you see this pulsar and its close companion white dwarf in orbit around their common center of mass. The animation zooms outward, showing this pair also in orbit with a more-distant, cooler white dwarf, and illustrates the motions of these three bodies. The entire system would fit within Earth's orbit around the Sun.
This clip seeks to explain the apparent paradox of skiers appearing "in the back seat" in the transition, based on a visualization of playing catch with a heavy "medicine ball," then recognizing that skiing is analogous to our skis playing catch with our center of mass in exactly the same way.
The first test of a cable-mounted camera rig that I designed and built in one day. The main part of the rig is a three degree of freedom wooden framework, which is held in place using butterfly nuts. Two pulleys (which are actually second-hand door runners) are attached to the top cross-piece of this wooden framework. The whole thing hangs off a piece of tensioned stranded steel cable, using a pair of carabiners clipped over the cable to secure the camera safely in the event of the pulleys running off the cable. The design is such that the camera's center of mass hangs vertically beneath the cable, no matter what orientation it has. The camera is a Canon XH-A1. Total cost of the rig (including the steel cable): AU$110. Two main problems exist with this rig: vibration and sway. The vibrat...
Educator Physics Courses, Center of Mass