Biomechanics & Movement — all lessons

Levers, torque and moment arms

How muscles and external loads create rotation at joints — torque, moment arms, mechanical advantage and lever classes — and why exercise difficulty changes through a range of motion.

Intermediate Evidence: Established consensus 3 min read Reviewed 2026-10-31 Status: draft

Learning objectives

  • Calculate torque from force and moment arm
  • Identify the three lever classes and their trade-offs
  • Explain how internal and external moment arms change through a movement
  • Use moment-arm reasoning to modify exercises and explain sticking points

Before this lesson

Why this matters

Exercise difficulty is not just about weight. Where the weight sits relative to each joint — its moment arm — determines how hard each muscle works. This is the mechanical basis of exercise selection, technique choices and progression.

Fundamental concepts

Torque (N·m) = force (N) × moment arm (m)Moment arm = perpendicular distance from the axis of rotation to the line of action of the force.
  • Internal torque — produced by muscles (muscle force × its moment arm).
  • External torque — produced by gravity on body segments and loads, or other external forces.
  • Rotation occurs in the direction of the net torque [neumann2017].

Lever classes

Three classes of lever in the body Three beams. First class: the fulcrum lies between the effort and the load. Second class: the load lies between the fulcrum and the effort. Third class: the effort lies between the fulcrum and the load, which is the most common arrangement in the human body and favours speed and range of motion over force. Torque equals force multiplied by its perpendicular moment arm. First class E · F · L F L E Head on the atlanto-occipital joint:neck extensors balance the head MA can be >1, =1 or <1 Second class F · L · E F L E Often taught: heel raise (toes = fulcrum).Its classification is debated. MA > 1 — force advantage Third class F · E · L F L E Elbow flexion: biceps inserts near theelbow; load is held in the hand MA < 1 — speed & range advantage F = fulcrum (joint axis) · E = effort (muscle force) · L = loadMA = mechanical advantage = effort arm ÷ load arm · Torque = force × perpendicular moment arm
Figure 1. The three classes of lever and their mechanical trade-offs. — Original diagram, FSHP Academy (schematic, not to scale).

Most muscles insert close to the joint with the load further away — third-class levers with mechanical advantage below 1. Muscles must generate forces several times larger than the external load, but small muscle shortening produces large, fast movement of the hand or foot [knudson2007].

Changing moment arms

  • External: in a dumbbell curl, gravity acts vertically, so the external moment arm is greatest with the forearm horizontal — the hardest point. Cables and bands change this profile.
  • Internal: muscle moment arms also change with joint angle (e.g., the patella increases the quadriceps moment arm).
  • Multi-joint lifts: in a squat, trunk angle and knee travel shift the external moment arms between hip and knee. More forward knee travel and an upright trunk increase knee demand; a more inclined trunk and less knee travel increase hip and back demand.

Practical application

Common mistakes and misconceptions

Assessment and practical tools

Sticking-point analysis: film a lift from the side, freeze at the slowest point and estimate joint moment arms. Strengthening the joint with the largest demand there (or modifying the lever) often helps.

Case study

A client struggles with lateral raises at 6 kg. Instead of reducing load, the trainer cues a slight elbow bend — shortening the moment arm — and progresses to straight arms over four weeks.

Further learning: video lessons

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Knowledge check

Knowledge check · 0/5

1. A 100 N load held 0.3 m from the elbow axis (forearm horizontal) creates an external torque of…

Answer B. 100 N × 0.3 m = 30 N·m.

2. In a standing dumbbell curl, external torque on the elbow is greatest when…

Answer B. The moment arm of gravity’s pull is longest when the forearm is horizontal.

3. Most muscle–bone levers in the body are…

Answer C. Effort is applied between the axis and the load, favouring speed and range.

4. Allowing more forward knee travel in a squat tends to…

Answer A. Knee travel lengthens the external moment arm at the knee and shortens it at the hip.

5. Mechanical advantage less than 1 means…

Answer A. Short effort arm relative to load arm — typical of third-class levers.

Short-answer & application questions

  1. Explain why a front squat is more knee-dominant than a low-bar back squat.
  2. How could you make a lateral raise easier without reducing the dumbbell weight?
  3. Describe the strength curve of a push-up and how bands might change it.

Key takeaways

  • Torque = force × perpendicular moment arm; joint rotation depends on net torque.
  • Most body levers are third class — they trade force for speed and range.
  • External moment arms change through a movement, creating the exercise’s resistance profile.
  • Small technique changes (bar position, knee travel, trunk angle) redistribute torque among joints.

Connected topics

References

  1. Neumann DA (2017). Kinesiology of the Musculoskeletal System: Foundations for Rehabilitation (3rd ed.). Elsevier. Textbook check pending
  2. Knudson D (2007). Fundamentals of Biomechanics (2nd ed.). Springer. Textbook check pending

Educational content only — not medical advice. Consult a qualified clinician for diagnosis or treatment.