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Yo-yo and unwinding cylinder
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Combine translation and rotation with tension torque.
For a cylinder unwinding from a string, a = g/(1 + I/mR²) down; for a solid disc a = 2g/3. Tension T = mg/3.
The yo-yo falls slower than free fall.
Rotation and translation are linked by a = αR.
In more detail
A yo-yo or a cylinder unwinding from a string both rotate and translate, with the string providing a torque. Their acceleration depends on their moment of inertia and the radius of the axle.
Real-world uses
- Yo-yo tricks depend on controlled unwinding and rewinding.
- Cable reels and winches use the same principle.
- A yo-yo or a cylinder unwinding from a string both move down while spinning, which combines translation and rotation.
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Frequently asked questions
Why does the yo-yo go up?
Because the string tension provides a torque that spins it, and the yo-yo winds back up.
Does the acceleration depend on the outer radius?
It depends on the axle radius and moment of inertia, not only the outer radius.
Why does a yo-yo go back up?
Its spin keeps the string unwinding past the lowest point, so it rises again once the rotation has enough angular momentum.
Related topics in Rotational Motion
Torque on a dipole · Pulley with mass · Atwood with real pulley · Angular impulse · Static friction in rolling · Slipping to rolling transition