Gravitational Potential Energy to Kinetic Energy

Question

When a yo-yo is released from a height $h$, the gravitational potential energy is converted to kinetic energy. However, the yo-yo obviously has less acceleration than $g$, $9.8frac{m}{s}$. This means that the final speed of the yo-yo is less than what it would be if it were in free fall. It seems that the kinetic energy at the end is less than the potential energy at the beginning. What happened to the rest of the energy?

garyp · Accepted Answer

The "missing" kinetic energy is still there ... it's now in the rotation of the yo-yo.

Daniela B · Answer

that energy most likely became thermal energy due to friction

John Darby · Answer

As @garyp said, the "missing" kinetic energy is that of rotation. Here is some additional information that should help you. Assuming the yo yo rolls down its string without slipping, the translational kinetic energy of the center of mass (CM) plus the rotational energy of the rotating yo yo about its CM equals the difference in potential energy (based on initial height minus final height of the CM). See Consistent Approach for Calculating Work By Friction for Rigid Body in Planar Motion on this exchange; specifically, the example for rolling without slipping down an inclined plane.

Answered by John Darby on April 20, 2021

Gravitational Potential Energy to Kinetic Energy

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