Laws of Mechanical Action

As further basis we have proved laws of mechanical motion. The form in which they are stated here was selected with a view toward their relationship to the problems of piano-technique. The laws of mechanical action as stated here are viewed in relation to piano technique.

1. A body at rest remains at rest unless acted upon by an external force.
2. A change in speed or direction of motion of a body results from the action of a second force, the first force producing the original motion.
3. The total effect of a force depends upon three things:
   1. Its numerical value,
   2. Its direction, and
   3. Its point of application.
4. The action of forces need not always produce motion. Two forces, equal and opposite, neutralize each other and do not produce motion.
5. The speed and direction of a body, unless the component forces be known, is not in itself an index of the forces acting upon the body.
   A force of 5 in the absence of all other forces will produce the same motion in a given body as a force of 10 opposed by a force of 5, other things equal.
6. The numerical value of a force^[1] depends upon the mass and the speed of the body producing it.
7. A force always produces motion in the exact line of its action, unless otherwise interfered with.
8. The force of gravity influences all motion. It acts vertically downward. Its value and direction are constant, the former for any given locality, the latter for all localities.
9. Rectilinear vs. Curvilinear Motion: Motion that takes place along a straight line is called rectilinear motion.
   Motion along a curved line is called curvilinear motion.
   When a body turns upon any axis, real or theoretical, motion of rotation results.
   When a body as a whole changes its spatial relationship to surrounding bodies, motion of translation results.
   Both types of motion may be present at the same time, in equal or in unequal degrees.
10. A force whose effect is the combined effects of several forces is called their resultant. ^[2]
    The forces producing the resultant are called the components.^[3]
11. The mutual reactions of two bodies on each other are always forces equal in amount and opposite in direction.

[1]Newton's Second Law: Force = mass X acceleration.

F = ma

[2]resultant: The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram.

[3]components: Draw coordinate axes on the free-body diagram. Decompose the forces acting on the object into x and y components. Calculate the x and y components of the resultant force by adding the x and y components of all forces. Finally, find the magnitude and direction of the resultant force by using its x and y components.