# Planet Roton

From a spring Honors Physics quiz. I’ve tried to erase as much as possible from the student’s corrections (green pen) and my notes (blue pen).

In the comments—

- What was the student thinking? How did he or she decide to make these particular marks on the paper?
- What question or problem would you pose next to help the student make the next step toward understanding?

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I’m not even sure I’m seeing all the mistakes in this one.

The first one that jumped out at me was the conversion error (1600km -> 16000m), which isn’t all that important to this particular problem, but, combined with the failure to express the answer in scientific notation, suggests to me that the student doesn’t have a good sense of the scale of this system. Not sure if I’d bother trying to correct this at this point.

The second error I saw was using centripetal acceleration instead of linear acceleration. In spite of having drawn a diagram that might be read as showing that the student understood the initial conditions, the student reached for the formula (I suspect) most often used with universal gravitation problems. I would ask about the directions of v_c and F_g, and then what happens to an object that starts out with v_c=0m/s if the only force is radial.

The third error I saw was in the LOL diagram. With Roton outside the system diagram, there’s no U_g for the second L. [If we include Roton in the system (and remember that G is negative), the approach might work: initial energy is zero, final gravitational energy is negative, leaving the kinetic energy to be positive. I’d want to assume that the meteorite is small enough that Roton didn’t accelerate noticeably during the process, so that all of the kinetic energy belongs to the meteorite, because otherwise I can’t separate the two easily.] I would ask the student what U_g is, when we include it in a system, and how the initial and final Ls are related.

The fourth error I noticed was using g at the surface as the acceleration the whole way in (and the units error on g). Again, I think the student grabbed for a nearby formula without thinking about the physical situation. I would ask the student what each part of the formula means and when it applies: does it apply at the beginning of the problem when the meteorite is at a (near infinite) distance/in the middle when the meteorite is speeding towards Roton/at the end when the meteorite is just about to crash into the surface of the planet.

I feel like I’m missing some things, both about what the student was thinking, and about how to solve the problem at a pre-calculus level…

I wonder why the planet is named “Roton”? Possibly this signaled to the student the idea of “rotation” and that’s how they got started down that path.