# How does this action in this picture reduce $R$? (Angular Momentum)

I was doing a course on Brilliant today when I came across this question:

In the picture, the question asks me what actions that must be done in order to maximize the distance I travel during takeoff from the curved ramp, and presents me with three choices: Stand up , Duck down or Do nothing.

I was really puzzled by this question so I went to get the explanation instead. This was what came up:

The correct answer was to stand up. However, after getting the explanation, I was still puzzled about how standing up will "shorten the radius of the curve around which she is traveling". (I do know that "shortening the radius of the curve around which she is traveling" will reduce R and will let the biker's velocity increase. I am puzzled about how that action can reduce R) Can anybody help?

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## 2 Answers

$$R$$ is the distance from the center of the circle to the center of mass. By standing up, you raise the center of mass and consequently shorten $$R$$. The center of mass is the average position of the mass of a body. If a force acts on the center of mass of any body, the body will only accelerate lineraly, but not rotationally. The center of mass of a person is roughly in their center, i.e. at about half their height. For a kneeling person, that might be 50cm from the ground, but for a standing person 80-90cm. $$R$$ is the only relevant distance in this system when calculating the angular momentum, so shortening it while keeping the angular momentum $$L$$ constant in fact increases $$v$$.

• Hi, thanks for answering! I almost got it... but can you define center of mass (in a beginner-friendly sort of way)? Thanks! :) – Jeffrey10th Oct 4 '18 at 10:04

There is nothing right in your explanation. Angular momentum is not constant along the ramp because there is a torque created by gravity. Velocity at the top is governed by energy considerations.

At best, I would suggest start the ramp standing, and end the ramp low. This way you minimize increase in potential energy.

• Hi, thanks for answering :) I'm not sure if this helps, but this was actually the full explanation: i.imgur.com/OG8RvVz.png Thanks for taking your time to help! – – Jeffrey10th Oct 4 '18 at 10:01