The other day I was recollecting about the time where childhood-me had bought a cheap plastic yo-yo from a “vending machine” and then as I was playing with it (this was my first time playing with the yo-yo), it hit the floor and broke into two pieces. This makes me wonder, how does a yo-yo work?
In our discussion of rotational motion, we touched on the concepts of linear and angular momentum. Linear momentum is defined as p = mv (where m is the mass of the object in kg and v is the velocity of the object in m/s), whereas angular momentum is defined as L = Iω (where I is the moment of inertia and ω is the angular velocity – it can be also defined as L = mvR, where R is the radius of the object).
We’ve also touched on Kinetic and Potential energy and we’ve learned that they are inversely proportional to each other. KE is defined as ½ mv2 (where m is the mass of the object and v is the velocity) and PE is defined as mgΔh (where g is 9.81 m/s2 and Δh is the height). Conservation of Energy is explored and thus we can choose to solve for the velocity of the yo-yo.
What is interesting about the yo-yo is that it has not only two potential energies, but also builds two momentums. There is the initial PE – which is 0J – but there is another PE that is built as the yoyo winds back up; this is cycled as it moves along the yo-yo. On similar grounds, the linear momentum of the yo-yo increases as it goes up-and-down and builds angular velocity as well.
How does it stop? There is Friction present as the yo-yo moves along the rope and as it moves, it slows it down. Sometimes when playing, the yo-yo will just hit the bottom of the extended rope but keep rotating/spinning (this is because the rope is loosely tied at the axle which allows for the spinning).
Even though we won't think about physics while playing with a yo-yo, it's really cool to see rotational dynamics and energy conservation in these toys!
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