Energy and Momentum Methods for Rigid Bodies in Plane Motion

Newtons second law in determining kinetics relationships is not always
the most ef?cient, although it always works. As for particles, energy
and momentum methods are often useful to analyze
rigid bodies in plane motion.

Work of a Force on a Rigid Body

The work of a force acting on a rigid body moving from position 1 to 2 is

Work of a Moment

The work of a moment has a similar form, for angular positions ?,

In the common case where the moment vector M is perpendicular
to the plane of motion,
M ? d? = M d?.
It is important to note those forces that do no work:
1. Forces that act at ?xed points on the body do not do work.
For example, the reaction at a ?xed, frictionless pin does no work
on the body that rotates about that pin.
2. A force which is always perpendicular to the direction of the
motion does no work.
3. The weight of a body does no work when the bodys center
of gravity moves in a horizontal plane.
4. The friction force ^ at a point of contact on a body that rolls
without slipping does no work. This is because the point of contact
is the instantaneous center of zero velocity.
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