Does the rotational speed of a planet consistently become faster and faster given that there are no conflicting events?
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The question in ill-stated and open to multiple interpretations. I'm going to answer two of them.
Assuming that by planet you mean a more-or-less solid object (like the Earth), then no. Conservation of angular momentum means that unless acted on by a non-central outside force the speed of rotation remains forever the same.
Assuming that the planet is an warm, gaseous object (like Jupiter shortly after the formation of the solar system), than the system is supported in part by Virial heating, and will continue to contract as it cools. Because Angular momentum is conserved in this system too, as the body contracts it's speed of rotation will increase. Eventually however, the contraction will stop as processes other than thermal pressure in the gas begin to dominate. Once that happens we're back to the first case: the rate of rotation is fixed.
A planet with no forces acting on it will rotate at the same speed for ever.
However a real planet will experience tidal forces which will eventually slow it's rotation until the same side always faces the sun (or possibly until it reaches a resonance with the sun's influence and other nearby large planets)
No, it will continue to rotate at the same rate forever. This is a consequence of angular momentum conservation.
Your question does lack a few specifics, but it's not at all incomprehensible? Common sense indicates that your initial premise must come from a basic example taught in public schools. That is that if you launch a rocket or spacecraft into outer space, it will continue to accelerate faster and faster. But unlike an orbiting planet which is defined by conservation of angular momentum, a rocket has a propulsion system with certain differing variables in each application. Although the immediate answer is no. I would recommend rephrasing your question after reviewing angular moment
The answer is 'No'. If you have to answer at school then the previous answers are fine, consistent whith mainstream.
The answer is 'Yes' under this undiscussed model (page 11, Rotation, eq 38) where the variation of LOD (Earth's Length Of Day) is discussed. A less known fact is that the Earth is increasing the long term rate of rotation, i.e. shorter days (image from here). The angular momentum redistribution due to tidal effects is not enough to account for the measures, because it implies a slowing instead of an acceleration of rotation. The overall redistribuition of water/ice and movement of the solid crust is also not sufficient to account for the measures.
My personal answer is 'Yes' because I can not find a single reason to disproof that model .
The extreme rotational speed of millisecond pulsars can be easily explained by model, as suggested there.