Moment arm

A moment arm is the perpendicular distance from a force’s line of action to the fulcrum.^{1Haff and Triplett (eds.), Essentials of Strength Training and Conditioning, 4th ed., p. 36.} Other names include force arm, lever arm and torque arm.^{1Haff and Triplett (eds.), Essentials of Strength Training and Conditioning, 4th ed., p. 36.} Torque equals force multiplied by its moment arm; for a muscle, that force is muscle tension.^{2Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 77.},^{3Zatsiorsky, Kraemer and Fry, Science and Practice of Strength Training, 3rd ed., p. 53.}

At a joint, the load and the muscle each have a moment arm.^{4Haff and Triplett (eds.), Essentials of Strength Training and Conditioning, 4th ed., p. 38.},^{5Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 61.} With free weights, the load’s moment arm is the horizontal distance from the weight’s center of mass to the joint, so it changes during the movement.^{4Haff and Triplett (eds.), Essentials of Strength Training and Conditioning, 4th ed., p. 38.} The muscle’s moment arm is the shortest perpendicular distance between the joint axis and its line of action; it’s largest when the angle of pull on the bone is 90 degrees.^{5Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 61.}

In practice

• A free weight’s moment arm is greatest when the limb is horizontal and falls to zero when the weight is directly above or below the joint.^{2Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 77.} Body position changes where it peaks: near 90 degrees of knee flexion in a standing leg curl, but at the start in a supine leg curl.^{2Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 77.}
• In a squat, leaning the trunk forward lengthens the moment arms at the hips and ankles and shortens them at the knees.^{6Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 78.} That increases demand on the hip extensors and plantar flexors and reduces demand on the knee extensors.^{6Schoenfeld and Snarr (eds.), NSCA’s Essentials of Personal Training, 3rd ed., p. 78.}
• Muscle leverage changes through the range of motion.^{7Zatsiorsky, Kraemer and Fry, Science and Practice of Strength Training, 3rd ed., p. 55.} One measurement of the biceps brachii’s long head found a moment arm of 11.5 mm at full elbow extension and 45.5 mm at 90 degrees of flexion, a fourfold difference.^{7Zatsiorsky, Kraemer and Fry, Science and Practice of Strength Training, 3rd ed., p. 55.}
• Tendon insertion affects the lever system: an insertion farther from the joint gives a longer moment arm and more torque, at the cost of movement speed.^{4Haff and Triplett (eds.), Essentials of Strength Training and Conditioning, 4th ed., p. 38.}