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0593_C10_fm Page 327 Monday, May 6, 2002 2:57 PM

Introduction to Energy Methods 327

A question that arises, however, is how do we determine n, the unit vector parallel to
the axis of rotation of B? To answer this question, recall the example of the previous section
where a particle P was pushed along a circular helix. In that example, we obtained the
direction of motion of P from the velocity vector. In like manner, the instantaneous axis
of rotation of body B is parallel to the angular velocity ωω ωω of B. Then, in Eq. (10.3.3), n is
given by:

n =ωωωω (10.3.4)
/
Because angular velocity is a measure of the rate of change of orientation, we see that
ωω ωω may be identified with dθ/dt. Hence, we may also express the work of Eq. (10.3.3)
in the form:

t *
∫
⋅
W = T ωω dt (10.3.5)
0
where t is the time of action of T. Observe the similarity of Eqs. (10.2.13) and (10.3.5).
*

10.4 Power

Power is defined as the rate at which work is done. That is,

P = dW dt (10.4.1)

For a force F doing work on a particle or body, the power of the force may be obtained
by differentiating in Eq. (10.2.13):

P =⋅Fv (10.4.2)

where v is the velocity of the point of application of F.
Similarly, for a couple doing work on a body, the power developed by the couple may
be obtained by differentiating in Eq. (10.3.5):

P = T ωω (10.4.3)
⋅

where, as before, T is the torque of the couple and ωω ωω is the angular velocity of the body.

10.5 Kinetic Energy

Kinetic energy is probably the most familiar and most widely used of all the energy
functions. Kinetic energy is sometimes described as energy due to motion.