KIN 322 Kinesiology · Unit 1: Foundations and the axial skeleton · on Exam 1
1.4 Levers, torque and biomechanics
Study notes for Levers, torque and biomechanics in KIN 322 Kinesiology at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in Mathub.
Big ideas
- Torque (moment of force) = force × the perpendicular distance from the axis to the force’s line of action (the moment arm). Units: N·m. A muscle or load makes the most torque when it acts at right angles to the segment.
- Levers are named by what sits in the middle. First class: axis in the middle (nodding the head at the atlanto-occipital joint; triceps pulling on the olecranon). Second class: resistance in the middle (a wheelbarrow; rising onto the toes is the usual body example). Third class: effort in the middle (biceps at the elbow and most limb muscles).
- Mechanical advantage = effort arm ÷ resistance arm. Above 1 (second class) favors force; below 1 (third class) favors speed and range of motion. Muscles attach close to joints, so they must pull with forces many times the load but move the hand or foot fast and far.
- Static equilibrium: the forces and torques on a segment each sum to zero. To hold a load still, muscle force × muscle moment arm = load × load moment arm (plus the segment’s own weight × its moment arm).
- Newton’s laws: inertia, F = ma, and action–reaction (the ground reaction force). A muscle’s pull splits into a rotary component (perpendicular, making torque) and a stabilizing or dislocating component (along the bone), and the split changes with joint angle. A low center of gravity over a wide base of support is more stable.
Key formulas
Torque
$$\tau = F \cdot d_{\perp}$$
Rotational equilibrium
$$\sum \tau = 0$$
Mechanical advantage
$$\text{MA} = \dfrac{d_{\text{effort}}}{d_{\text{resistance}}}$$
Worked example
A 20 N dumbbell is held 0.30 m from the elbow with the forearm horizontal. The biceps inserts 0.04 m from the elbow and pulls straight up. Ignoring the forearm’s weight, what biceps force holds it still?
Show the solution
Torques balance about the elbow: F × 0.04 = 20 × 0.30, so F = 6 ÷ 0.04 = 150 N. The muscle pulls 7.5 times the load because its moment arm is 7.5 times shorter (MA = 0.04 ÷ 0.30 ≈ 0.13).
Common mistakes
- Using the distance along a slanted bone instead of the perpendicular distance to the line of force.
- Classifying a lever by where the muscle is. Ask what is in the middle: axis, resistance or effort.
- Thinking a mechanical advantage below 1 is a design flaw. Third-class levers trade force for speed and range.
Exam tipRemember “ARE 1-2-3”: the item in the middle is the Axis for first class, the Resistance for second and the Effort for third.
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