Does holding weights allow you to run faster? I'm not talking about training with weights so that when you run without them your muscles are used to pushing more weight so with less weight it'll be easier, I'm talking about while actually holding them.
So this question arose when I decided to carry some light weights (1 kg) as I went for a fast jog: I noticed how easy it was to run faster while holding the weights which got me thinking.
I figure that it would allow you to run faster for the same sort of reasons that we swing our arms in the first place but now it's just multiplied somewhat. Running with weights in your hands will allow you to conserve angular momentum far better which means you should be able to move your legs at a faster rate, i.e. some more of the work is being done by the arms. Moving your left arm back will contribute to moving your right leg forward, so the more momentum that is in your arm the easier it should be correct? Obviously this only works with light weights as if the weight slows down your arm movements you may actually lose momentum. Are my conclusions correct?
I also guess that this will also tire out your legs more as you are pushing around more weight.
Does this all mean that sprinters should train their arms a lot in order to run faster with the higher mass causing more momentum with each swing of the arms?
 A: Ernie is close to the correct answer, but the fundamental thing that needs to be considered is how the internal energy of the body flows. I researched this in a very interesting book I''m still reading, Principles of Animal Locomotion . Chapter 7 addresses running and section 7.5 discusses Internal Kinetic Energy . Limb accelerations can store kinetic energy and the compression of muscles, tendons and ligaments can store potential energy as elastic recoil. The book presents data and analysis that examines the gait of a four legged animal, the balance of external and internal energy, but basically the principles can also apply to a human running. The answer to your question is yes. Holding weights can help balance the flow of energy between the internal kinetic energy of your swinging arms and the elastic recoil of your leg muscles which can increase your forward spring and thus your speed.
But nothing is ever free. You are also right that it will take extra energy to support the weights which could tax energy in the long run. So speed increases, endurance is spoiled.
A: Speculating here...
I suspect that for light weights the answer is yes - with the right technique. Your center of mass moves up and down which requires energy being absorbed and expended by your legs. Moving your arms with small weights should allow you to even out the motion, lowering the peak stress on your legs so they tire more slowly. In a sense you are storing some of the energy in your arms. It might require more energy expenditure over all, but this is spread out over more muscles so each muscle tires less. This in turns means they will be less likely to produce lactic acid - and thus you use your fuel store more efficiently.
A: Consider your arms as pendulums.  The period of a pendulum is determined by its length and by gravity.  Though the period is affected neither by the weights nor by the amplitude of your arms, these two quantities affect your balance and efficiency.
When you run you get into a rhythm of arms and legs.  Your legs are do the work; your arms are along for the ride, except to the extent they help you balance and move the rest of your body in harmony with your legs.
BUT, if you change the length of your arm pendulum by moving its center of mass by adjusting the bend in your elbows, you adjust the period and may allow your arms more effortlessly to follow the period of your legs. The weights may allow you to accomplish this with greater precision.  They may facilitate subconscious fine-tuning.
AND, you may be able to reduce the amplitude of your arms, while keeping the correct period, by shortening the pendulum.  The less the amplitude of your arms, the less energy will go into them, and the more energy will be available for your legs.
Small weights in your hands may make this whole process more precise, more efficient, and more effective.
Here is a graphic exposition on the physics of pendulums: http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c4.  Scroll down to the box labelled "Pendulum Geometry".
