Would a 50 lb weight on the end of rope twist faster from a tree branch than a 10lb weight? How does weight afftect motion?

Yep.  Weight affects the motion for sure.  Imagine if it were a feather that was on the rope instead of a heavier weight.  So I can answer the last part of this question but I have NO idea how it works and why.  I ain't no scientific mathmeticianal genius like our president.  

Assuming the weights are solid cylinders and of the same diameters, I don't think the heaver ones would twist faster, but would twist further, thanks to their greater mass giving them greater momentum acting against the elasticity of the rope.

Their radii must be equal though. If one is of larger radius it will twist more slowly than the narrower ones due to a natural law called the Conservation of Angular Momentum. An impressive display of that is given by the figure-skater who starts spinning on one point: draws the arms in and spins rapidly, extends the arms straight out to slow down.


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A parallel is the simple pendulum: if you were to let these metal weights swing gently instead of twist, then provided the length from the suspension-point to the centre of mass of the weight is equal for all those metals, their periods (time of one complete swing) will be the same.

Galileo Galilei is credited with discovering that law, and is said to have observed it initially by using his own pulse to time a slight-swinging chandelier in a church. It led to him realising it is length not mass that affects the period, hence his making the first pendulum-controlled clock "escapement". .This proved far more accurate than the flywheel-type escapements used previously, which depended on pure momentum of a weighted iron arm rotating first one way than the other; rather than the harmonic oscillation of a pendulum.

(A spring-controlled clock or watch uses the harmonic vibration of a spiral spring, alternately partly winding and unwinding.)


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The apparent conundrum of a rock and feather falling at the same rate is right in principle, because the acceleration due to gravity is constant irrespective of mass.

It is close to 32feet/second^2. Or these days, 9.8metres/second^2, to obey the International Standards Organisation and the law of most countries now.

However the feather would fall more slowly because its large surface area versus its very small mass, and its shape, means greater air resistance against its fall; and its aerodynamics would make it glide or flutter down rather than dropping in a straight line.

A better demonstration would be given by a rock and closed bag of feathers - a pillow, say. Or a tennis-ball weighing an ounce or two and a cannon-ball weighing, say, 20lbs. And yes, before anyone says anything, I know I should have used grammes or kilogrammes!