How Moment Arms Affect Powerlifting.
DISCLAIMER
The following is quite a complicated concept to explain and imagine… well, for me it is anyway 🙂
So, I’m going to do my best to simplify this for the masses… and myself!
Two terms that we need to understand here are: FORCE and MOMENT.
FORCE
Force = Mass x Acceleration.
Force is measured in Newtons. One newton is the force required to accelerate an object with a mass of 1kg 1 meter per second per second, in the same direction as the applied force (i.e. linear).
The per second per second bit (aka. per second squared, or S2) can be challenging to get your head around as time is seemingly a linear concept, it doesn’t have extra dimensions in it. So to help visualise this, imagine the following:
You’re driving a car and accelerate at 10metres per second, each passing second. That is to say that:
After ONE second, your speed is 10 metres per second.
After TWO seconds, your speed is 20 metres per second.
After THREE seconds, your speed is 30 metres per second.
Now for the purpose of most lifting, what is important here is the fact that FORCE is considered to be LINEAR (i.e. things being pushed or pulled in a straight line). Imagine pulling a car with a rope that’s on a fixed path which runs parallel to the ground.
MOMENT
Moment = Force x distance from fixed axis (or pivot).
A moment is the turning force around a fixed pivot, measured in Newton Metres (Nm). This is because FORCE is measured in Newtons, and DISTANCE is measured in Metres – hence, Nm. In the case of moments, the distance must be the perpendicular (90°) distance from the pivot to force.
See the image below to see the difference between FORCE and MOMENT when tightening a nut.
N.B – the fixed pivot can also be referred to as the axis, or axis of rotation! In the case below, the nut is the axis, or fixed pivot.
Torque/Moment
When a moment acts, it results in a TURNING/ROTATIONAL force. You may also see this referred to as ‘Torque’, however strictly speaking the correct use of either terminology depends on the context.
Mathematically, moment and torque are the same thing – both refer to a force acting perpendicular to a distance to cause rotation.
It is the mechanical effect of that force which dictates which term should be used. Simply put… torque twists, moment bends.
Torque is specific to rotational motion, causing objects to rotate around an axis (i.e. torque twists), it is subjected to shear stresses.
Moment however is the tendency of a body to rotate about a specific axis (i.e. moment bends), it is subjected to normal stresses – these being tensile and compressive stresses.
Another way to differentiate the two is to consider that moment makes an object move (like the seesaw example below), but not specifically rotate. Torque however always results in a rotational effect on an object around an axis.
Imagine a steel rod fixed at it’s central point. If you apply a force to the end point of the rod, it starts to turn and rotate – this is due to torque. If however you change the point of fixation of the rod to its end (imagine fixing one end to a wall, making it a cantilever), then apply a downward force to the other end, it will bend downwards – this is the moment.
N.B. – I would say that when it comes to reading up about forces acting on muscles and joints, try not to get bogged down on which term is used. I’ve read far too many articles that use both terms interchangeably.
Now, if something is balanced then the moments are said to be equal and opposite. For example, imagine a heavy child and a light child sitting on a balanced seesaw.
To maintain balance, the lighter child will need to be sitting further away from the pivot, and the heavier child will need to sit closer to the pivot – in this case, the fixed pivot is the middle of the seesaw.
Force & Moment with Weights
Now, let us take the principles of FORCE and MOMENT and apply them to lifting weights. Thank you in advance to Stronger by Science, who produced an excellent article on how to bench press.
FORCE in terms of lifting weight
Imagine bench pressing 180kg. The 180kg represents the mass component of FORCE (remember, FORCE = Mass x Acceleration).
If you weren’t supporting the bar, it would accelerate downward at 9.8m/sec2 (due to gravity).
So that is to say the bar is exerting 1764 Newtons of force downwards.
Your hands/arms would therefore be subjected to 1764 Newtons of force (180kg x 9.8m/s2 = 1764N).
The direction of the force is linear. This is the direction that gravity is pulling – straight down. Similarly, when our muscles contract, they exert a force pulling one end of the muscle straight toward the other end.
MOMENT in terms of lifting weight
Now remember, moment is force applied about an axis (aka. a fixed pivot). While force is linear, moment is rotational.
Imagine bicep curling a 20kg barbell. Your upper arm is straight down by your side, and your forearm (which is 30cm/0.30m long) is parallel to the floor.
To calculate the FORCE the barbell is exerting straight down, it would be:
20kg x 9.8m/sec2 = 196N of force, directed straight down to the ground.
Then to calculate the MOMENT the barbell is exerting at the elbow (the elbow being the fixed pivot), you multiply 196N by the distance (in metres) between the barbell and your elbow.
(The distance between the barbell and your elbow is called the MOMENT ARM).
In this case, it would be: 196N x 0.30m = 58.8Nm.
Since this moment is exerted downward, which would extend the elbow with the forearm in this position, and we’d call this an extensor moment.
If you wanted to continue curling the bar up, you’d need to produce a flexor moment greater than 58.8Nm with your biceps and brachialis. Get it?
Now since the moment arm is the distance between the fixed pivot and the load;
If the elbows were either a bit more flexed or a bit more extended, then:
- The MOMENT ARM would be shorter
- The MOMENT would be smaller
*even though the forearm would be the same length.
Dig deep into that grey matter, reunite with that GCSE Trigonometry, and look at the example below to visualise this. Get your SOHCAHTOA’s out!
*Sidenote – Moments imposed by a load on your musculoskeletal system (like the example above) are called external moments. Moments produced by your muscles pulling against your bones are called internal moments.
Internal Moments
These are calculated the same way external moments are.
The FORCE component is the contractile force of the muscle.
The MOMENT ARM is the distance a muscle attaches from the centre of the joint (fixed pivot) that it’s moving.
That can be represented as:
Muscle Contractile FORCE x Muscle Moment Arm = Internal Flexor Moment.
For example, if the patellar tendon (which transmits the FORCE of the quadriceps to the tibia) inserts 5cm/0.05m from the centre of the knee joint, and the quads contract hard enough to exert 10,000N of force perpendicular to the tibia, the internal extensor moment would be:
10,000N x 0.05m = 500Nm.
Hopefully that’s cleared up ‘What is a moment arm in terms of powerlifting?‘
If you’d like to see how these principles apply to the bench press, see our article here for further information.
References
Math Is Fun (2024) Math Is Fun. Available at: https://www.mathsisfun.com/physics/moment-torque.html (Accessed 04/07/2024).
FuseSchool (2024) FuseSchool – Global Education. Available at: https://www.youtube.com/channel/UCS3wWlfGUijnRIf745lRl2A (Accessed 04/07/2024).
Greg Nuckols (no date) Stronger By Science. Available at: https://www.strongerbyscience.com/how-to-bench/ (Accessed 04/07/2024).
Ortho Info (2024) American Academy of Orthopaedic Surgeons. Available at: https://orthoinfo.aaos.org/en/diseases–conditions/patellar-tendon-tear/ (Accessed 04/07/2024).
Yavus, H.U., & Erdag, D. (2017) ‘Kinematic and Electromyographic Activity Changes during Back Squat with Submaximal and Maximal Loading’, Applied Bionics and Biomechanics. Available at: https://www.researchgate.net/publication/316699385_Kinematic_and_Electromyographic_Activity_Changes_during_Back_Squat_with_Submaximal_and_Maximal_Loading (Accessed 04/07/2024).
Whilst not writing for FGUK, Tim works as a Physiotherapist, Personal Trainer and is a Retired Ammunition Technician with the British Army. In his spare time Tim enjoys engaging in a whole variety of sports, spending considerable time with his little rascal of a dog, relaxing with his friends and family, but most of all.. geeking out on all things fitness!
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