General Work

Energy Balance

Rigid Body Work - Energy Terms

The Principle of Work and Energy equates the total work performed on a body to the change in kinetic energy,

     Σ Work = Δ Kinetic Energy

Another way to express this concept is

T1 + ΣU1-2 = T2

     T1 = kinetic energy (translational and rotational)
                at position 1
     T2 = kinetic energy (translational and rotational)
                at position 2
     ΣU1-2 = total change in energy (i.e. work)
                   between positions 1 and 2

Work on a rigid body is the same as work on a particle, with the addition of rotational energy. Recall from Particle Energy Methods section, there are various ways to model energy for a particle. These are listed in the table at the left.


Rotating Rigid Body
  Work of a Force Couple, or Moment


The work of two parallel, non-collinear forces in opposite directions with equal magnitudes forms a couple and moment. This moment generate energy similar to a linear force through a distance. However, the distance is now the angle of rotation.

    Kinetic Energy for a Rotating Body

Rotational and Translational
Kinetic Energy


For a particle that has no rotation, the kinetic energy is simply,

     T = 1/2 m v2

This equation can be applied to every particle that makes up a rigid body,


However, if the particle is a rigid body with dimensions, then the velocity needs to be written as


where G is the center of gravity. The second terms models the rotation of the object. Substituting vi into the kinetic equation and noting that a magnitude of vi/G = ri/G ω gives

T = 1/2 m vG2 + 1/2 IG ω2

If the rigid body has a fixed point, then the equation becomes

     T = 1/2 Io ω2

where Io is moment of inertia about the fixed point.

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