In #MESExperiments 30 I continue with the the GyroTop magnetic spinning top from Experiments 28 and 29, and this time showcase that it behaves the same way with gravity as it does with magnetic attraction. I demonstrate this by turning the GyroTop side-ways and then slowly extending it outwards so that the magnetic attraction becomes less while the downward force of gravity plays a more dominant role. One would expect that the spinning top would fall downwards as it extends further away from the magnetic but counterintuitively it rises upwards against gravity! This is similar to its tendency to move opposite of the magnetic attraction, and the direction the GyroTop points can be considered as opposite of the vector sum of both gravity and magnetism. Truly remarkable stuff! The timestamps of key moments of the experiment are listed below. 1. Spinning up the GyroTop: 0:00 2. Gradually Extending the GyroTop from a Horizontal Position: 0:33 3. Gradually Pulling Back the GyroTop from its Risen Position: 1:14 4. Extending the GyroTop Even Further: 1:21 5. Pulling Back the GyroTop Again: 1:45 6. GyroTop Hits the Magnetic Base: 1:57 Stay tuned for #MESExperiments 31... View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/mesexperiments-30-magnetic-spinning-top-aligns-opposite-of-gravity-and-magnetism View more experiments! - #MESExperiments video series: https://peakd.com/mesexperiments/@mes/list - DRAFT #MESExperiments video series: https://mes.fm/experiments-draft Related Videos: #MESScience video series: https://mes.fm/science-playlist #AntiGravity video series: https://peakd.com/antigravity/@mes/series #FreeEnergy video series: https://mes.fm/freeenergy-playlist ?#MESExperiments 28: Magnetic Spinning Top Aligns Opposite of Magnetic Attraction: https://peakd.com/hive-128780/@mes/mesexperiments-28-magnetic-spinning-top-aligns-opposite-of-magnetic-attraction ?#MESExperiments 27: Spin Friction Can Make Gyroscope Rise from Steep 70° Angle (No Casing Rotation) ?#MESExperiments 25: Increasing Spin Friction Can Make Gyroscopes Rise Much Faster: https://peakd.com/hive-128780/@mes/mesexperiments-25-increasing-spin-friction-can-make-gyroscopes-rise-much-faster ?#MESExperiments 13: Steepest Gyroscope Rising Experiment Ever! 74 Degrees from the Vertical: https://peakd.com/mesexperiments/@mes/mesexperiments-13-steepest-gyroscope-rising-experiment-ever-74-degrees-from-the-vertical-magic ?#MESExperiments 3: Gyroscopes Exert 'Inertial Forces' With ZERO Loss of Spin Rate: https://peakd.com/mesexperiments/@mes/mesexperiments-3-gyroscopes-exert-inertial-forces-with-zero-loss-of-spin-rate-freeenergy ?#MESScience 1: How Does a Powerball Gyroscope Work? + Gyros Are Inverted Pendulums: https://peakd.com/messcience/@mes/messcience-1-how-does-a-powerball-gyroscope-work-gyros-are-inverted-pendulums ☝#AntiGravity Part 6: Objects in Rotation Defy ‘Mainstream’ Physics + MES Duality Concept: https://ecency.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=rVX4pVWbI84

This is part 1 of the series on Transformations of Functions and in this video I look at transforming a basic function by vertically or horizontally shifting it. This is very useful for graphing and also to better understand how equations are written and their corresponding graphs. Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiodo45BXtkWowIxNmw #HIVE video notes: https://peakd.com/hive-128780/@mes/transformation-of-functions-part-1-vertical-and-horizontal-shifts Related Videos: Transformations of Functions Part 2: Horizontal Stretching and Reflecting: http://youtu.be/8sUgreHjTt8 Transformations of Functions - Graphing Sine and Cosine Example: http://youtu.be/9stMcSBo2mo . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a very unique problem on showing that the n-th partial sum of the harmonic series is NOT an integer. The harmonic series is the sum of the terms 1/i where i is a positive integer. To show that the partial sum is not an integer, we require some truly outside-of-the-box thinking, which fortunately for us is made easier with the given hint. To prove this, we first assume that the partial sum IS an integer and then observe what happens to 2 similar equations. The first is the multiplication of (the product of all odd integers less than or equal to n) * (the largest power of 2 that is less than or equal to n) * (partial sum). The second equation is the same as the first but with the assumption that the partial sum is an integer. After going over some very unique mathematical reasoning, I show that the left side of the equation is always odd while the right side is always even. This is a contradiction and thus the partial sum can not be an integer! Pretty epic brain twister! The timestamps of key parts of the video are listed below: - Problem 26: Partial Sum of Harmonic Series is NOT an Integer: 0:00 - Solution: 2:27 - Right side of hint equation is even: 4:16 - Left side of hint equation is odd: 7:23 - Checking when r is less than k: 13:41 - Checking when r = k: 16:56 - Summary: Partial Sum of Harmonic Series is NOT an integer: 20:45 This video was taken from my earlier video listed below: - Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg - HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=AknFzsQ1dZU

In this video I go over another example on determining the amount of work done in moving an object using integrals and this time I look at pulling a rope from the top of a building. In this example, the force required to pull the rope up is not given but we can determine the force and hence the work by breaking the rope into many small pieces and then use integration to determine the equation and hence amount of work required to pull up the rope. The reason we need to consider the rope as many small pieces is because as the rope is pulled up the length of the rope changes and thus the amount of force required keeps decreasing as the length of rope being pulled up decreases. Download the notes in my video: http://1drv.ms/1CFoEb3 View Video Notes on Steemit: https://steemit.com/mathematics/@mes/integrals-and-work-example-3-pulling-a-rope Related Videos: Integrals and Work: Example 2 - Hooke's Law: http://youtu.be/h8lwvB9rOng Integrals and Work Example 1: http://youtu.be/YO0M0w12URo Integrals and Work: Introduction: http://youtu.be/dNmfGmWyMqc Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk Fundamental Theorem of Calculus - Proof of Part 1 of the Theorem: http://youtu.be/CAqTwiPxYwU . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=Koy5vZxzR9U