Body force
A body force is a force that acts throughout the volume of a body, in contrast to contact forces.
Gravity and electromagnetic forces are examples of body forces. Centrifugal and Coriolis forces can also be viewed as body forces.
This can be put into contrast to the classical definition of surface forces which are supposed to be exerted to the surface of an object. Shear forces and normal forces occurring in physical and engineering circumstances are supposed to be surface forces and exerted to the surface of an object. All cohesive surface attraction and contact forces between objects are also considered as surface forces.
Definition
A body force is simply a type of force, and so it has the same dimensions as force (mass times length per time squared). However, it is often convenient to talk about a body force in terms of either the force per unit volume or the force per unit mass. If the force per unit volume is of interest, it is referred to as the force density throughout the system.
A body force is distinct from a contact force in that the force does not require contact for transmission. Thus, common forces associated with pressure gradients and conductive and convective heat transmission are not body forces as they require contact between systems to exist. Radiation heat transfer, on the other hand, is a perfect example of a body force.
Examples of common body forces include:
-
- Gravity
- An electric force acting on an object that is charged throughout its volume
- Magnetic forces acting on currents within an object, such as the braking force that results from eddy currents
Inertial forces (often called "fictitious forces") can be viewed as body forces. Common inertial forces are
-
- Centrifugal force
- Coriolis force
- transverse force or Euler force, which occurs in a rotating reference frame when the rate of rotation of the frame is changing
- It is worth noting that inertial forces are not actually forces. Rather they are corrections to Newton's second law when it is formulated in an accelerating reference frame.
Acceleration
Like any other force, a body force will cause an object to accelerate. For a non-rigid object the acceleration of a volume element would be found by
,
where 
is the density of the substance at point 
and (lowercase) f is the force density. This is simply Newton's second law formulated to apply to a small volume element.
In the case of gravity a(r) is simply the gravitational field.
The entirety of the body force acting upon a system can be found by integrating the force density throughout a volume of interest.
,
where dV is an infinitesimal volume element and f is the force density within the system.