Reference Frames
Two observers, one on a moving train. Builds on Projectile Motion.
You're standing inside a train moving smoothly at 100 km/h. You throw a ball forward at 20 km/h (relative to you).
How fast is the ball moving according to someone standing on the platform outside?
120 km/h! In classical mechanics, velocities simply add: v(ground) = v(train) + v(ball). The ball is already moving at 100 km/h with the train, so throwing it at 20 km/h adds to make 120 km/h.
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Toggle between the train rider's view and the platform observer's view. Same physics, different perspectives.
v' = v + V
This breaks down near light speed! Einstein showed that c + c = c, not 2c. But for everyday speeds, Galilean addition works perfectly.
A plane flying at 900 km/h into a 100 km/h headwind moves at only 800 km/h relative to the ground. That's why flights take longer one way!
Einstein imagined lightning striking both ends of a moving train. The train rider and platform observer disagree about simultaneity — the birth of special relativity.
To cross a river straight, you must aim upstream. Your velocity relative to land = your swimming velocity + the river's current velocity.
“Physics doesn't care which frame you use — the laws are the same. Choose the frame that makes the problem simplest. That's not cheating; it's physics.”
Frame Switcher
Set up a scenario with moving objects, then switch between reference frames to see how everything changes — except the physics.
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Set the train speed to match the ball speed. In the ground frame, the ball appears stationary after being thrown backward!
There is no 'absolute rest.' You can always find a frame where any object is stationary. Motion is relative.