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What kind of software the instructor used in this video in order to make these circular and uniform motions beside pen writings.

It seems like he has defined circular and linear paths for the objects to move while he was illustrating the lesson.

I need to know what similar softwares I can use to achieve this beside my pen writings while I'm recording the screen to make an educational video.

Notes: I have asked the author of the video, but it seems he is inactive replying to comments.

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It's a bit unclear, how many different simulations you need and whether you want to create your own ones or not. Creating own simulations can be a time consuming task, since you need to define which parameters shall be included in the simulation or not. That could be:

  • friction, often neglected for educational purposes
  • temperature
  • air pressure
  • humidity

That said, there are some solutions with predefined simulations online and browsers should be able to provide the required touch support:

My Physics Lab is a browser based physics simluator. It has a Pendulum. Setting the gravity to 0, you can move it with your mouse like in the linked video.

Phet offers physics simulations as well. It also has a Pendulum, but not exactly as in the video.

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As mentioned in my other answer, many physics simulations are programmed in order to perform specifically the task expected for the tutorial.

A contributor of Khan Academy, 3Blue1Brown, answers in his FAQ that he uses Python and the Manim library to animate math tutorials. You could combine that with a physics library like Pymunk.

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