Using hair to measure acceleration due to gravity

Using hair to measure acceleration due to gravity

Gravity exerts a force on every object which is proportional to its mass. The amount by which it is proportional is the value g or the acceleration due to gravity. On the surface of the earth g is 9.8 meters per second per second and this is the rate that an object will accelerate when it’s in freefall. Now the value of g will vary a little bit depending on where you are, mostly to do with altitude and the value of 9.8 is an average and it has actually been measured quite precisely, but today we’re going to throw precision out the window and attempt to measure g using human hair. First let’s talk about pendulums. A simple pendulum consists of a metal sphere on a long thin string. One period of oscillation will be the time it takes for this mass to go from, say here, through one complete cycle and back to where it started. We can work out the period T from this formula here 2 pi times the square root of L, which is the length of our pendulum, over g, which is our acceleration due to gravity. Note that the period doesn’t depend at all upon the mass and just know that this formula was derived using an approximation that sin(theta) is equal to theta So it’s only valid for small angles say less than about 15 degrees. We can rearrange this formula for g if we know our length and our period. Experimentally if you have a longer length then you’re going to have a longer period which may reduce the significance of errors when you’re trying to time the period, so what better to use as a length of the pendulum than some of my hair? I am going to attach a mass to the end to provide some tension force that will allow it to oscillate. I don’t personally drink but I found this nice bottle opener, which I think will be appropriate. Now the big assumption here is that my hair doesn’t weigh very much compared to the mass i’m going to put on the end. I’m assuming that the center of mass of the pendulum is still going to be in this metal spot on the end and I’m also assuming that my hair stays a constant length throughout which may not be true in practice but I’m hoping we’ll be an OK approximation here. To get my hair as close to massless as possible I haven’t included all of it for the pendulum just a small amount and I’m going to measure the length of the pendulum as the distance from the top of my hair tie down to where I think the center of mass of this metal part is. I got some help measuring the length and found it to be 90 centimeters with an uncertainty of two centimeters. Then I released the hair at an angle and timed five oscillations. This makes it easier to measure one period by dividing the time by five afterwards. I repeated this part of the experiment twice more and got an average period of 1.9 seconds with an uncertainty of 5 milliseconds. Putting my values into the formula for g I get g equal to 9.8 plus or minus 0.7 meters per second squared and that’s actually pretty good especially since this is far from a high-tech science lab. Some of the possible sources of error include measuring the distance to the center of mass, assuming that my hair is massless and also assuming that it travels out a perfect 2d shape when in reality I think it travels out a bit of an ellipse. There’s also some uncertainty in the measurement of the period of oscillation. If you wanted to make this experiment a bit more accurate you could try using various different values of L for the length of the pendulum and then finding a line of best fit to find our value of g but this was pretty alright for some quick backyard physics. Now, this video is sponsored by So if you would like to have some fun with science, you can go to and sign up for free. They have a course on gravitational physics so that might be a great place to learn a little bit more about the subject discussed here. The first 200 people to go to that link can get 20% off an annual premium subscription so I’d recommend brilliant as a fun way to learn more about some of the concepts that I’ve discussed here. If you enjoyed this video then please consider subscribing to my channel and I’ll see you next time.

🦋Escucha a tu corazón, no te rindas, ese dolor que hoy sientes en tu interior, se irá

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100 Replies to “Using hair to measure acceleration due to gravity”

  1. Thanks (and happy birthday) to my brother Jack for his appearance in this video.

    At 3:00 the uncertainty in the period is 50ms. And the unit for L should be m. Check out the description for a link to error analysis (as done in a past JEE exam)

  2. It would be nice if you make a video about measurement uncertainty and how to add, subtract, multiply and divide numbers with significant figures , professor Walter Lewin once said in one of his MIT lectures: ''any measurement that you make without the knowledge of its uncertainty is completely meaningless''.

  3. Hmm couple of mistakes there Toby :-1) The pendulum touched your skirt so the time period measured is not correct.
    2)and L=0.90 + or – 0.02 m not cm hehe lol

  4. If we had a beautiful girl like her to teach gravity while in our elementary… we wouldn't have lost many Newtons today 🙁

  5. I like how your videos are straight to the point. No asking for likes before the actual content and i even learn something from the vids. Keep it up.

  6. A solid ball of radius .005m and desnity 2.5×10³ kg/m³ is dropped into a lake water to measure it's depth. The ball reached the bottom of the lake in 10sec . If the ball attained terminal velocity in 9sec , determine the depth of the lake.[ Coefficient of viscosity of water is 1.6×10-³ Nsm-²]

  7. You look like Karl Rock's sister.
    Sorry I can't understand much now cuz I changed from science to commerce. But can relate some to previous knowledge

  8. Dude could you do a video on torque and momentum, and…. basically just do a video for every physics subject. Pls Thanks

  9. Im a high school student in Canada and im interested in physics, especially theoretical physics. I just want to know the process I have to go through to become a theoretical physics. So I have to do an undergraduate in physics. Then do I continue "everything" physics or do i get to choose between experimental and theoretical. And when do I get affiliated with a certain theory are there specific courses or is it after i do university, like research and stuff.

  10. I want to tell you how much I love your videos. You have reignited my excitement for physics and maths.  In 1969, I was a freshman student majoring in Physics at University. On my first test I scored a 94 and the next highest test score was 70. But each consecutive test was lower and lower because I was not prepared by my high school education for mathematics above algebra and felt handicapped and way behind my peers. This destroyed my self-confidence. I began to believe the University system in math and physics was clearly structured to give a marked advantage to those gifted at memorization and regurgitation not understanding. As a sophomore I
    moved to Computer Science out of desperation. I hope you continue to find time to produce such excellent content. I support several YouTubers in Science, Physics and the Creative Arts with Patreon. I would encourage you to do so as well.

  11. What is your definition of mass for this video? How fast does an object accelerate in water? Why isn't it the same? Does gravity act differently in water?

    Why doesn't an ironmongers anvil accelerate at all when dropped in mercury? It actually floats…does gravity not affect an ironmongers anvil?

    Why does the definition of "neutral buoyancy" not mention gravity?

    You don't know what you're talking about kidda…

  12. You're one of the most intelligent and gorgeous people to ever own a youtube channel. Such a pleasure to listen to and learn from.

  13. How much does air drag affect your result if at all?
    As a young physicist you could go down in history like Einstein if you could figure out gravity and how to turn it off and on like a light switch.


  15. Hey Tibees I'm Panwell from SA, uhm I am currently studying Applied Geology(1st year) and I wanna be an Astronomer so I wanted to know which choices will be best for me 1. Majoring in physics( and doing lot of math) 2.Just change and go straight to Astrophysics.

    If I choose to major in physics, have a degree in it wouldn't be a long process for a person who wanna be an astronomer?

  16. Creo que si subtitulas al español los videos y hacer colaboraciones con "Date un Voltio", "CdeCiencia","El Robot de Platón", "QuantumFracture" vas a ganar varios millones de suscriptores.

    How you solve physics problem and maths complex problems like approach and imagining and minor steps came in your mind while solving them and how should other should do this so that they also can answer questions with ease

  18. your videos are great, i am a student and it really helped me in understanding physics up to some extent. please please, make a video on gyroscope..🙏

  19. Mam…
    Plzzzz u r a best guide for me ..
    Plzzz upload a video on Simple Hormonic Motion for NEET examination…(basics)

  20. You explain so good. Do take one fundamental topic – Thermodynamics (being my favourite), please explain some interesting phenomenons. Would be highly appreciable. Thank you!!

  21. due to the little weigth of human hair, it should be difficult to measure the time more than a few seconds, and more to replicate the Foucault's pendule…lol ( evidence of tge earth's rotation)

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