Who Reaches the Goal First? | Gold vs. Silver | Physics of Motion on an Inclined Plane | C4D4U

Here is another little physics experiment. Gold against silver on an inclined plane. I'm looking forward to your answers. You can find the answer here in the description if you were wrong about the result. Why Does a Gold Sphere Roll Down at the Same Speed as a Silver Sphere? In this video, you’ll see two spheres of the same size—one made of gold, the other of silver—rolling down a 45-degree incline over a distance of one meter. Surprisingly, under ideal conditions, they arrive at the bottom simultaneously. Here’s why: Same Geometry, Same Acceleration When a sphere rolls without slipping, the acceleration depends on its geometry (specifically, the ratio of its moment of inertia I to m*r^2), not on its mass or density. For a solid, uniformly dense sphere (regardless of whether it’s gold, silver, or another material), that ratio is 2/5. Because both spheres share the same shape and size, they have the same ratio and thus the same acceleration. The Key Equation The translational acceleration a of a sphere rolling down an incline of angle alpha without slipping can be written as: a = [g * sin(alpha)] / [1 + (I / (m * r^2))] Since (I / (m * r^2)) = 2/5 for a uniform sphere, the equation simplifies to: a = [g * sin(alpha)] / [1 + (2/5)] = (5/7) * g * sin(alpha) This shows both gold and silver spheres will accelerate at the same rate. Other Factors In the real world, minor differences in surface friction or air resistance might create tiny deviations, but under near-ideal conditions—and assuming no slipping—both spheres reach the bottom at the same time. Conclusion Despite being made of different materials (and therefore having different weights), two solid spheres of the same size roll at the same rate when they have the same distribution of mass. It’s the geometry and uniformity—not whether the sphere is heavier or lighter—that determines how fast they accelerate and how quickly they reach the bottom. 💖 Together for more creative animations! 💖 I'm glad you enjoy my animations! If you'd like to support my work, you can leave a small contribution via PayPal ( https://paypal.me/c4d4u ) or use the Super Thanks button. Every bit of support helps create new, creative videos. But even a like, a comment, or sharing means a lot – thank you for being part of this! 😊 ♥️♥️♥️-----------♥️♥️♥️-----------♥️♥️♥️ ASMR for your eyes. Most of my videos help to relax a bit. I would be happy if you like my videos and enjoy them. My recommended playlists: Only C4D4U Softbody Simulations: https://www.youtube.com/watch?v=jNqT8qkJY4U&list=PLUiMrVMtq6VFIC1HTv8QeNPWV_8pXDO6o All my C4D4U Simulations / Animations: https://www.youtube.com/watch?v=N3mbPvZ_xXc&list=PLUiMrVMtq6VF9wIcoBaXi4ePjCki8uQ4x !!! Please do not copy my videos. Any copy will result in copyright infringement. In the last few months I have had to report several hundred copyright infringements. There are already so many people who have no ideas of their own and create exactly the same content (really absolutely identical content incl. objects, titles, descriptions). Images were also used for advertising without permission. All take, none give back. This is really very sad and of course makes me sad. !!! My Equipment: https://c4d4u.one/my-equipment/ In the future I will learn more Blender and Houdini FX. Blender is very cool and free. ******************************* ❤️❤️❤️ Official Website: https://c4d4u.one TikTok: https://www.tiktok.com/@c4d4u Twitter: https://twitter.com/C4D4U Facebook: https://www.facebook.com/C4D4U-420803691739156 Instagram: https://www.instagram.com/c4d4u/ ******************************* ❤️❤️❤️ Relax and enjoy this video. ASMR for my eyes. Some people make it happy and satisfied. It also has a calming effect. ASMR = Autonomous sensory meridian response C4D4U: Animations and any Cinema 4D tutorials https://www.youtube.com/c/C4D4U MUSIC-MODE ;) Why don't I enter the music title anymore. Well, unfortunately some people not only copy my animations (because they have no ideas of their own) but even use exactly the same music. These people may now search for it themselves ;) I hope for your understanding. #physics #physicsexperiment #physicseasy