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A yo-yo goes up and down due to the principles of angular momentum and gravity.
When you throw the yo-yo down, the spinning motion of the yo-yo creates angular momentum. This angular momentum causes the yo-yo to resist being pulled back up immediately. Gravity also pulls the yo-yo downwards.
As the yo-yo reaches the end of the string, the angular momentum and gravity cause it to slow down. At this point, the upward pull of the string overcomes the downward pull of gravity, and the yo-yo starts to climb back up the string.
The cycle then repeats, with the yo-yo going down due to gravity and angular momentum, and then back up due to the string’s upward pull and the decreasing downward momentum. This up and down motion continues as long as the yo-yo is spinning quickly enough to maintain the angular momentum.