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Calculus is used to determine the force of gravity and the gravitational potential energy between an object and a planet, inside and outside the planet. Equations and graphs are determined and discussed. Want Lecture Notes? This is an AP Physics C: Mechanics topic. Content Times: 0:01 Basic universal gravitation equations 1:07 Outside the planet 1:42 Assumptions for inside the planet 3:38 Deriving mass inside r 4:23 Determining the equation for force of gravity inside the planet 5:24 Graphing the force of gravity inside the planet 5:59 Determining the equation for universal gravitational potential energy inside the planet 7:37 Solving for the constant C 8:49 The equation for universal gravitational potential energy inside the planet 9:41 Looking over the graphs Multilingual? Please help translate Flipping Physics videos! Previous Video: Impulse for Two Objects being Attracted to One Another Please support me on Patreon! Thank you to Sawdog, Christopher Becke, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

 universal gravitational potential energy
 function
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Name: Force of Gravity and Gravitational Potential Energy Functions from Zero to Infinity (but not beyond) Category: Circular Motion & Gravity Date Added: 20180311 Submitter: Flipping Physics Calculus is used to determine the force of gravity and the gravitational potential energy between an object and a planet, inside and outside the planet. Equations and graphs are determined and discussed. Want Lecture Notes? This is an AP Physics C: Mechanics topic. Content Times: 0:01 Basic universal gravitation equations 1:07 Outside the planet 1:42 Assumptions for inside the planet 3:38 Deriving mass inside r 4:23 Determining the equation for force of gravity inside the planet 5:24 Graphing the force of gravity inside the planet 5:59 Determining the equation for universal gravitational potential energy inside the planet 7:37 Solving for the constant C 8:49 The equation for universal gravitational potential energy inside the planet 9:41 Looking over the graphs Multilingual? Please help translate Flipping Physics videos! Previous Video: Impulse for Two Objects being Attracted to One Another Please support me on Patreon! Thank you to Sawdog, Christopher Becke, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Force of Gravity and Gravitational Potential Energy Functions from Zero to Infinity (but not beyond)

 universal gravitational potential energy
 function
 (and 6 more)

The mechanical energy of a satellite in circular orbit is solved for in terms of universal gravitational potential energy. And the velocity of the satellite is compared to escape velocity. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:14 Types of mechanical energy of a satellite 1:21 Solving for the velocity of a satellite in circular orbit 2:34 Solving for the mechanical energy of a satellite 3:31 Comparing satellite velocity to escape velocity Next Video: Impulse for Two Objects being Attracted to One Another Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving Escape Velocity of Planet Earth Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

 universal gravitational potential energy
 derive
 (and 9 more)

Name: Mechanical Energy of a Satellite in Circular Orbit Category: Circular Motion & Gravity Date Added: 20180304 Submitter: Flipping Physics The mechanical energy of a satellite in circular orbit is solved for in terms of universal gravitational potential energy. And the velocity of the satellite is compared to escape velocity. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:14 Types of mechanical energy of a satellite 1:21 Solving for the velocity of a satellite in circular orbit 2:34 Solving for the mechanical energy of a satellite 3:31 Comparing satellite velocity to escape velocity Next Video: Impulse for Two Objects being Attracted to One Another Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving Escape Velocity of Planet Earth Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Mechanical Energy of a Satellite in Circular Orbit

 universal gravitational potential energy
 derive
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Escape velocity is defined and illustrated. The escape velocity of planet Earth is derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:42 Defining escape velocity 1:43 Conservation of mechanical energy 3:22 Initial and final mechanical energies 5:38 The escape velocity of planet Earth 6:19 Relating this to binding energy Next Video: Mechanical Energy of a Satellite in Circular Orbit Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving the Binding Energy of a Planet Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

 potential energy
 universal gravitational potential energy
 (and 4 more)

Name: Deriving Escape Velocity of Planet Earth Category: Circular Motion & Gravity Date Added: 20180225 Submitter: Flipping Physics Escape velocity is defined and illustrated. The escape velocity of planet Earth is derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:42 Defining escape velocity 1:43 Conservation of mechanical energy 3:22 Initial and final mechanical energies 5:38 The escape velocity of planet Earth 6:19 Relating this to binding energy Next Video: Mechanical Energy of a Satellite in Circular Orbit Multilingual? Please help translate Flipping Physics videos! Previous Video: Deriving the Binding Energy of a Planet Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Deriving Escape Velocity of Planet Earth

 potential energy
 universal gravitational potential energy
 (and 4 more)

Deriving the Binding Energy of a Planet
Flipping Physics posted a video in Circular Motion & Gravity
Binding energy of a planet is defined and derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:21 Defining binding energy 0:48 Proving change in gravitational potential energy equals work done by force applied 3:03 Universal gravitational potential energy 3:39 The binding energy of a planet 5:16 An alternate way of solving this problem Next Video: Deriving Escape Velocity of Planet Earth Multilingual? Please help translate Flipping Physics videos! Previous Video: Universal Gravitational Potential Energy Introduction Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.
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 nonconstant
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Name: Deriving the Binding Energy of a Planet Category: Circular Motion & Gravity Date Added: 20180218 Submitter: Flipping Physics Binding energy of a planet is defined and derived. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:21 Defining binding energy 0:48 Proving change in gravitational potential energy equals work done by force applied 3:03 Universal gravitational potential energy 3:39 The binding energy of a planet 5:16 An alternate way of solving this problem Next Video: Deriving Escape Velocity of Planet Earth Multilingual? Please help translate Flipping Physics videos! Previous Video: Universal Gravitational Potential Energy Introduction Please support me on Patreon! Thank you to Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Deriving the Binding Energy of a Planet

 planet
 nonconstant
 (and 5 more)

Universal Gravitational Potential Energy is introduced and graphed. It is compared to the force of gravity. And the “zero line” is defined. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:11 “Normal” gravitational potential energy 1:33 Gravitational fields 2:22 Universal Gravitational Potential Energy Equation 3:07 Comparing gravitational potential energy to force of gravity 4:12 Graphing Universal Gravitational Potential Energy 5:35 The “zero line” for universal gravitational potential energy 6:05 Can universal gravitational potential energy ever be positive? 6:49 Gravitational potential energy at the surface of the Earth 7:57 Three things to be careful of. Next Video: Deriving the Binding Energy of a Planet Multilingual? Please help translate Flipping Physics videos! Previous Video: Gravitational Field Introduction Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

 gravitational field lines
 field lines
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Name: Universal Gravitational Potential Energy Introduction Category: Circular Motion & Gravity Date Added: 20180212 Submitter: Flipping Physics Universal Gravitational Potential Energy is introduced and graphed. It is compared to the force of gravity. And the “zero line” is defined. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:11 “Normal” gravitational potential energy 1:33 Gravitational fields 2:22 Universal Gravitational Potential Energy Equation 3:07 Comparing gravitational potential energy to force of gravity 4:12 Graphing Universal Gravitational Potential Energy 5:35 The “zero line” for universal gravitational potential energy 6:05 Can universal gravitational potential energy ever be positive? 6:49 Gravitational potential energy at the surface of the Earth 7:57 Three things to be careful of. Next Video: Deriving the Binding Energy of a Planet Multilingual? Please help translate Flipping Physics videos! Previous Video: Gravitational Field Introduction Please support me on Patreon! Thank you to Dan Burns, Jonathan Everett, Christopher Becke, Sawdog, and Scott Carter for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Universal Gravitational Potential Energy Introduction

 gravitational field lines
 field lines
 (and 7 more)

The gravitational field is introduced and illustrated. For a constant field and a nonconstant field around a spherical object. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 The two force of gravity equations 0:55 The constant gravitational field equation 2:25 Gravitational Field Lines 3:16 What is a gravitational field? 4:33 The gravitational field equation around a spherical object 5:48 Drawing the field lines around a spherical object 7:02 Are gravitational field lines real? Next Video: Universal Gravitational Potential Energy Introduction Multilingual? Please help translate Flipping Physics videos! Previous Video: Number of g's or gForces Introduction Please support me on Patreon! Thank you to Tony Dunn, Christopher Becke and Jonathan Everett for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

Name: Gravitational Field Introduction Category: Circular Motion & Gravity Date Added: 20180205 Submitter: Flipping Physics The gravitational field is introduced and illustrated. For a constant field and a nonconstant field around a spherical object. Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:01 The two force of gravity equations 0:55 The constant gravitational field equation 2:25 Gravitational Field Lines 3:16 What is a gravitational field? 4:33 The gravitational field equation around a spherical object 5:48 Drawing the field lines around a spherical object 7:02 Are gravitational field lines real? Next Video: Universal Gravitational Potential Energy Introduction Multilingual? Please help translate Flipping Physics videos! Previous Video: Number of g's or gForces Introduction Please support me on Patreon! Thank you to Tony Dunn, Christopher Becke and Jonathan Everett for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Gravitational Field Introduction

Calculus based review of Universal Gravitation including Newton’s Universal Law of Gravitation, solving for the acceleration due to gravity in a constant gravitational field, universal gravitational potential energy, graphing universal gravitational potential energy between an object and the Earth, three example problems (binding energy, escape velocity and orbital energy), and Kepler’s three laws. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? At 6:01 this video addresses an error in the Universal Gravitational Potential Energy Graph from the video's previous iteration. Content Times: 0:10 Newton’s Universal Law of Gravitation 1:52 Solving for the acceleration due to gravity 2:02 Universal Gravitational Potential Energy 4:52 Graph of Universal Gravitational Potential Energy between an object and the Earth 6:01 Correcting the Universal Gravitational Potential Energy Graph 7:30 Binding Energy Example Problem 9:41 Escape Velocity Example Problem 11:19 Orbital Energy Example Problem 13:52 Kepler’s Three Laws 14:17 Kepler’s First Law 16:19 Kepler’s Second Law 16:42 Deriving Kepler’s Third Law Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Simple Harmonic Motion Review (Mechanics) Previous Video: AP Physics C: Rotational vs. Linear Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan, Sawdog, and Frank Geshwind for being my Quality Control team for this video.

 universal gravitation
 newtons universal law of gravitation
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Derive the acceleration due to gravity on any planet. Find the acceleration due to gravity on Mt. Everest. And determine how much higher you could jump on the top of Mt. Everest! Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 Deriving the acceleration due to gravity on any planet 1:54 Finding the acceleration due to gravity on Mt. Everest 3:16 How much higher could you jump on the top of Mt. Everest? Next Video: Altitude of Geosynchronous Orbit (aka Geostationary Orbit) Multilingual? Please help translate Flipping Physics videos! Previous Video: The Force of Gravitational Attraction between the Earth and the Moon Please support me on Patreon! Thank you to Aarti Sangwan and Christopher Becke for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

Name: Deriving the Acceleration due to Gravity on any Planet and specifically Mt. Everest Category: Circular Motion & Gravity Date Added: 20171211 Submitter: Flipping Physics Derive the acceleration due to gravity on any planet. Find the acceleration due to gravity on Mt. Everest. And determine how much higher you could jump on the top of Mt. Everest! Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:08 Deriving the acceleration due to gravity on any planet 1:54 Finding the acceleration due to gravity on Mt. Everest 3:16 How much higher could you jump on the top of Mt. Everest? Next Video: Altitude of Geosynchronous Orbit (aka Geostationary Orbit) Multilingual? Please help translate Flipping Physics videos! Previous Video: The Force of Gravitational Attraction between the Earth and the Moon Please support me on Patreon! Thank you to Aarti Sangwan and Christopher Becke for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. Deriving the Acceleration due to Gravity on any Planet and specifically Mt. Everest

According to NASA, the mass of the Earth is 5.97 x 10^24 kg, the mass of the Moon is 7.3 x 10^22 kg, and the mean distance between the Earth and the Moon is 3.84 x 10^8 m. What is the force of gravitational attraction between the Earth and the Moon? Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:56 Solving the problem 2:15 Determining how long until the Moon crashes into the Earth 4:00 Determining what is wrong with this calculation Next Video: Deriving the Acceleration due to Gravity on any Planet and specifically Mt. Everest Multilingual? Please help translate Flipping Physics videos! Previous Video: How Much is a Mermaid Attracted to a Doughnut? Please support me on Patreon! Thank you to Aarti Sangwan and Christopher Becke for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video.

Name: The Force of Gravitational Attraction between the Earth and the Moon Category: Circular Motion & Gravity Date Added: 20171203 Submitter: Flipping Physics According to NASA, the mass of the Earth is 5.97 x 10^24 kg, the mass of the Moon is 7.3 x 10^22 kg, and the mean distance between the Earth and the Moon is 3.84 x 10^8 m. What is the force of gravitational attraction between the Earth and the Moon? Want Lecture Notes? This is an AP Physics 1 topic. Content Times: 0:07 Translating the problem 0:56 Solving the problem 2:15 Determining how long until the Moon crashes into the Earth 4:00 Determining what is wrong with this calculation Next Video: Deriving the Acceleration due to Gravity on any Planet and specifically Mt. Everest Multilingual? Please help translate Flipping Physics videos! Previous Video: How Much is a Mermaid Attracted to a Doughnut? Please support me on Patreon! Thank you to Aarti Sangwan and Christopher Becke for being my Quality Control Team for this video. Thank you to Youssef Nasr for transcribing the English subtitles of this video. The Force of Gravitational Attraction between the Earth and the Moon

Name: AP Physics C: Universal Gravitation Review (Mechanics) Category: Oscillations & Gravity Date Added: 20171222 Submitter: Flipping Physics Calculus based review of Universal Gravitation including Newton’s Universal Law of Gravitation, solving for the acceleration due to gravity in a constant gravitational field, universal gravitational potential energy, graphing universal gravitational potential energy between an object and the Earth, three example problems (binding energy, escape velocity and orbital energy), and Kepler’s three laws. For the calculus based AP Physics C mechanics exam. Want Lecture Notes? At 6:01 this video addresses an error in the Universal Gravitational Potential Energy Graph from the video's previous iteration. Content Times: 0:10 Newton’s Universal Law of Gravitation 1:52 Solving for the acceleration due to gravity 2:02 Universal Gravitational Potential Energy 4:52 Graph of Universal Gravitational Potential Energy between an object and the Earth 6:01 Correcting the Universal Gravitational Potential Energy Graph 7:30 Binding Energy Example Problem 9:41 Escape Velocity Example Problem 11:19 Orbital Energy Example Problem 13:52 Kepler’s Three Laws 14:17 Kepler’s First Law 16:19 Kepler’s Second Law 16:42 Deriving Kepler’s Third Law Multilingual? Please help translate Flipping Physics videos! AP Physics C Review Website Next Video: AP Physics C: Simple Harmonic Motion Review (Mechanics) Previous Video: AP Physics C: Rotational vs. Linear Review (Mechanics) Please support me on Patreon! Thank you to Aarti Sangwan, Sawdog, and Frank Geshwind for being my Quality Control team for this video. AP Physics C: Universal Gravitation Review (Mechanics)

 universal gravitation
 newtons universal law of gravitation
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Using a toy car and a piece of paper we can visualize and understand relative motion by doing an introductory problem. Content Times: 0:13 Reading the problem 0:42 Translating the problem 1:38 Visualizing the problem 2:24 The vector diagram and equation 3:14 Isnâ€™t this vector addition? 3:30 Solving for the velocity of the car with respect to the Earth 4:44 Solving for the direction of the car with respect to the Earth 6:32 Part ( B) How far did the car travel? 7:15 New similar triangle with displacements 8:15 Solving part ( B) 9:58 Solving part (c) How long did the car travel? 10:58 An alternate solution to part (c) 11:36 Yes, it did take about 15 seconds Want [url="http://www.flippingphysics.com/relativemotionproblem.html"]Lecture Notes[/url]? Multilingual? Please help [url="http://www.flippingphysics.com/translate.html"]translate Flipping Physics videos[/url]! Next Video: An Introductory [url="http://www.flippingphysics.com/relativemotioncomponents.html"]Relative Motion Problem with Vector Components[/url] Previous video: [url="http://www.flippingphysics.com/introductiontorelativemotion.html"]Introduction to Relative Motion[/url] using a Quadcopter Drone [url="http://www.flippingphysics.com/give.html"]1Â¢/minute[/url]

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Name: An Introductory Relative Motion Problem Category: Kinematics Date Added: 29 September 2014  02:58 PM Submitter: Flipping Physics Short Description: None Provided Using a toy car and a piece of paper we can visualize and understand relative motion by doing an introductory problem. Content Times: 0:13 Reading the problem 0:42 Translating the problem 1:38 Visualizing the problem 2:24 The vector diagram and equation 3:14 Isnâ€™t this vector addition? 3:30 Solving for the velocity of the car with respect to the Earth 4:44 Solving for the direction of the car with respect to the Earth 6:32 Part ( How far did the car travel? 7:15 New similar triangle with displacements 8:15 Solving part ( 9:58 Solving part © How long did the car travel? 10:58 An alternate solution to part © 11:36 Yes, it did take about 15 seconds Want Lecture Notes? Multilingual? Please help translate Flipping Physics videos! Next Video: An Introductory Relative Motion Problem with Vector Components Previous video: Introduction to Relative Motion using a Quadcopter Drone 1Â¢/minute View Video

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Escape Velocity and its Applications
pavelow posted a blog entry in Blog Having Nothing to do with Physics
The calculation for escape velocity is a pretty simple conservation of energy problem. K at infinity =.5mv2 = 0 because v at infinity = 0 U at infinity = GMm/r = 0 at infinity because r = infinity K=0 U=0 K=U .5mv2 = GMm/r From there it's simple algebra, and escape velocity is ve = sqrt(2GM/r) This equation's applications are seen in the exploration of space. Spacecraft need to reach escape velocity in order to not eventually crash back into the earth's surface. Some satellites are orbiting earth at just above escape velocity, meaning that they are actually spiraling away from the planet. On the other hand, some satellites are orbiting just below escape velocity, meaning that they will eventually fall into the atmosphere and burn up. However, some of these satellites have onboard rockets which can change their trajectory, allowing for more stable orbits and longer lifetimes. The Voyager 1 spacecraft used its escape velocity to leave the solar system and explore what lies beyond. NASA's Curiosity mission required the spacecraft to reach near escape velocity (although I'm sure the actual spacecraft reached a higher speed) to make it to Mars. As humans explore more of the space that surrounds the planet, escape velocity and its applications will become even more important.
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