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Physics and real-world

Sections: Pure, Games, Geometry, Physics, Large.

If you make any progress on any of these puzzles, or if you'd like to contribute a new one, then please do tell me about it.

Puzzles in this section:

Bowling ball

Q: ??? Given the positions of the finger holes in a (spherical) wooden bowling ball, can we embed lumps of lead to make the ball fair? How unique is this solution?

"Fair" presumably means at least that

the centre of mass is at the centre of the sphere;
the moment of inertia is independent of the axis we choose.

Is this sufficient? Can we do even this?

In the 2D case is condition 1 enough?

[TB, 24 Jan 2002]

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Earth's angular momentum

Q: What should the earth's day length be such that its angular momentum (relative to the solar system) is 0?
[TB, 29 Nov 1999]

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Escape velocities

Q: What are the escape velocities for the earth, solar system and galaxy?
[29 Nov 1999]

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Home energy storage

Q: How much energy can a household store conveniently using a flywheel, eg to store summer solar energy for the winter?
[14 May 1997]

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Orbits under gravity

Q: In Kepler's Laws "radius" means the angular-averaged radius, but what's the time-averaged radius?

Q: What are the speed and period of a satellite orbiting at the earth's surface?

Q: If a (light) satellite in a circular orbit is suddenly stopped, how long does it take to hit the (point) mass it's orbiting?

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Sections: Pure, Games, Geometry, Physics, Large.