That article is correct but, as it's a practical example, it may be a bit fuzzy about the actual basics. The basic principle of moments is that length times force needs to be the same on both sides - the "Clockwise Moments equal the Anticlockwise Moments" when balanced (in Schoolboy language). Only a minimal extra force is needed to make the lift and, of course, as the weight is raised, it comes closer into the pivot so the radius gets less. The angle of the muscles on the skeleton will change and could even give a greater mechanical advantage*. Fair enough. But how do you actually define where the pivot is, inside your wrist or where the forces are acting in there? Levers don't need to be just in a straight line and what counts is the radius (called the perpendicular distance) around which the forces act. When you step on a bicycle pedal, you are pushing down on the crank but the chain is pulling horizontally - the mechanical advantage is still the ratio of the pedal length to the sprocket diameter. (Is this too basic? Sorry if it is.)
In the case of your hammer exercise, you have three pivots - wrist, elbow and shoulder. You can ignore the elbow joint, probably, because you can rotate the arm so the joint is locked.
Does it matter what you do to get the hammer vertical? No swinging allowed, presumably but what about dropping your arm to allow the wrist to point the hammer vertically and then lift your arm? That would make the job easier as your wrist could rotate the hammer to the vertical much more easily (like in clean and jerk) - hardly any force needed at all if you get the timing right. Then you'd be bringing the hammer weight a lot closer to your shoulder for the final lift.
If it has to be a straight arm lift, the actual muscle force needed to hold the hammer horizontal would be around:
Hammer weight X (total length of hammer plus arm) ÷ (one tenth of the length of your upper arm)
Sounds horrendous (around 1500 lbs)! But, as you lift it (haha) the muscle force should get less.
If you wanted to know the equivalent weight held directly in the hand, that would be
Hammer weight X (length of hammer plus arm) ÷ (length of arm)
About 40 lbs.
*Mechanical advantage: for muscles, working on bones and lifting a load, the mechanical 'advantage' is actually a fraction (less than one) - around 1/10, so it's a 'disadvantage' haha and the muscles need to be ten times stronger than the load they need to deal with. But it does mean that the end of your limbs can move a long way for a small muscle contraction.
