Work (physics) - Work of Forces Acting On A Rigid Body

Work of Forces Acting On A Rigid Body

The work of forces acting at various points on a single rigid body can be calculated from the work of a resultant force and torque. To see this, let the forces F1, F2 ... Fn act on the points X1, X2 ... Xn in a rigid body.

The trajectories of Xi, i=1,...,n are defined by the movement of the rigid body. This movement is given by the set of rotations and the trajectory d(t) of a reference point in the body. Let the coordinates xi i=1,...,n define these points in the moving rigid body's reference frame M, so that the trajectories traced in the fixed frame F are given by

The velocity of the points Xi along their trajectories are

where ω is the angular velocity vector obtained from the skew symmetric matrix

known as the angular velocity matrix.

The small amount of work by the forces over the small displacements δri can be determined by approximating the displacement by δr=vδt so

or

This formula can be rewritten to obtain

where F and T are the resultant force and torque applied at the reference point d of the moving frame M in the rigid body.

Read more about this topic:  Work (physics)

Famous quotes containing the words work, forces, acting, rigid and/or body:

    But he had gone his way, the grass all mown,
    And I must be, as he had been,—alone,

    ‘As all must be,’ I said within my heart,
    ‘Whether they work together or apart.’
    Robert Frost (1874–1963)

    By speaking, by thinking, we undertake to clarify things, and that forces us to exacerbate them, dislocate them, schematize them. Every concept is in itself an exaggeration.
    José Ortega Y Gasset (1883–1955)

    Often, when there is a conflict between parent and child, at its very hub is an expectation that the child should be acting differently. Sometimes these expectations run counter what is known about children’s growth. They stem from remembering oneself, but usually at a slightly older age.
    Ellen Galinsky (20th century)

    Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.
    Saul Kripke (b. 1940)

    I had wild Jack for a lover;
    Though like a road
    That men pass over
    My body makes no moan
    But sings on:
    All things remain in God.
    William Butler Yeats (1865–1939)