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Math Puzzle for January 31, 2025

Centrifuged right off the surface

Alameda Post - A math diagram of a small sphere resting on top of a larger sphere. In the diagram, an arrow indicates that the small sphere moves along the large sphere, and another small sphere is drawn to indicate its other location. The angle between the starting point and ending point of the small sphere, drawn from the middle of the large sphere, is theta.

A small sphere resting atop a large sphere begins to slide to the right.
The large sphere has a diameter of ten meters.
The small sphere has a diameter of one meter.
Initially the small sphere remains in contact with the large sphere.
Gathering speed, the small sphere breaks contact due to centrifugal force.
Find the angle θ at which the small sphere breaks contract with the large.
Assume no friction and no rotational kinetic energy in the small sphere.

First correct answer at [email protected] wins a Tucker’s gift card.

Last week’s winner was Roy Samuelson with A = 42 square units.

Jeff Smith is a former Math teacher and a retired US Navy Lieutenant Commander. Reach him at [email protected].

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