Equations of motion

The equations of motion permit us to model movements mathematically. One of the most useful equations comes from Newton's second law of motion, which states that the sum of all forces acting on an object is equal to the product of the object's mass and its rate of change of velocity, or acceleration.

An analogous equation for rotational movement relates the sum of moments acting on an object to the product of that object's moment of inertia around an axis of rotation and its angular acceleration.

The sum of moments, symbolized by the left side of this equation, is composed of a variety of individual moments, including

• ground reaction moments
• gravity and inertial moments
• joint moments, produced by forces in muscle and other soft tissue

Because many movements combine straight-line translational movement with rotation around some axis, we often must employ both equations.

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Last updated 2-2-98 ©Dave Thompson PT