Work-Energy relation for a rigid body

** **

** **

**Work of a force:** One calculates the work of
a force on a rigid body exactly the same as one would calculate the work of a
force for a particle. For a rigid body, the velocity used is the velocity of
the particle on the rigid body that the force is applied on.

_{}

**Power of a
couple:** The
power of a couple ** M** applied
on a rigid body having an angular velocity of

_{}

** **

**Work of a couple:**** **The work of a couple is the integral of its power over a time.

**Work of a couple
in 2-D:** The
work of a couple applied on a rigid body in two-dimensional motion is

_{}

**Kinetic energy of
a rigid body:**
The kinetic energy of a rigid body can be evaluated from one of the following
equations

_{}

**Work-Energy
relation:**** **The work energy relation for
a rigid body is given as

_{}

As
for a particle, one can use the potential energy to calculate the work of
conservative forces and use the alternate form of the work-energy relation
given by

_{}

**Potential energy:** The potential energy for a
constant gravitational acceleration is given by

_{}

where *h* is measured from a reference elevation
to the center of mass of the rigid body.

The potential energy of a spring is calculated exactly the same as
for a particle so that

_{}

where *k* is the spring
constant, *l* is the current length, *l*_{o} is the free length.

ã Mehrdad Negahban and the
University of Nebraska, 1999-2002.

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Department
of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526