# The Physics of a Yo-yo

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The Physics of a Yo-yo

In everything that we do, there is some aspect of physics involved in it. Even if we are just standing still on the ground, or leaning up against a wall, there are still numerous forces acting upon us. This paper will tell of the physics involved in throwing a yo-yo.

When you release a yo-yo, gravity acts on its center of mass to pull the yo-yo downward. Because the string of the yo-yo is wrapped around the yo-yo's axle, and because one end of the string is attached to your finger, the yo-yo is forced to rotate as it drops. If the yo-yo could not rotate, it would not drop.

Just as any object falling in a gravitational field, the rate of drop increases with time (it decreases 9.8 meters every second to be exact) and so, necessarily, does the rotation rate of the yo-yo. The rate of drop and the rotation rate are greatest when the bottom is reached and the string is completely unwound. The spinning yo-yo contains rotational kinetic energy taken from the gravitation potential energy through which the yo-yo has dropped.

Usually, the string is tied loosely around the axle so that the yo-yo can continue to spin at the bottom. Because the full length of the string has been laid out, the yo-yo can drop no further and, consequently, the rotation rate cannot increase further. If left in this condition, the friction between the axle and the string will eventually dissipate the energy of rotation or, equivalently, the rotational kinetic energy of the yo-yo and the yo-yo will come to rest.

However, a momentary tug on the string causes the friction between the string and the axle briefly to increase so that the axle no longer slips within the string. When the axle stops slipping, the rotational kinetic energy of the spinning yo-yo is large enough to cause the string to wind around the axle. This causes the yo-yo to begin to "climb" back up the string. After the first one or two rotations, the string can no longer slip, so the process of climbing up the string continues beyond the momentary application of the tug.

As the yo-yo continues to climb back up the string, the angular momentum (rotational kinetic energy) of the yo-yo is converted back into gravitational potential corresponding to the increasing height of the center of mass of the yo-yo.