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From personal experience, if you write the physics engine yourself you might find you never get around to making the game itself.

If your game loop is running at 60 fps then each frame exists for about 0.017 seconds. What happens if you have a 10 Kg weight sitting on your scale for the duration of half a frame (0.008 seconds), will your engine display 5 Kg on the scale, or what?

Interesting problems to solve, but can easily take up all your game development time.