interaction

When one object exerts a force that may change the state of motion (translational or rotational) of another object, those objects are said to interact.

Motivation for Concept

There are many ways that one object can change the motion of another. A person may kick a ball across the ground, giving it a translational motion, or instead may spin a ball on their finger, giving it rotational motion. The earth changes the motion of objects through the conservative action-at-a-distance of gravity as well as its electrostatic charge, and also through the nonconservative interaction of air resistance. Introductory physics incorporates several ways of describing interactions.

Common Interactions

Several specific interactions are commonly encountered in mechanics.

• contact force — A force that arises when one macroscopic body presses against another.
• gravitation (universal) — An interaction between two massive particles resulting in an attractive force exerted on each by the other.  The force is proportional to the gravitational constant G = 6.674 28(67) x 10-11 m3 kg-1 s-2, and the masses of the bodies, and inversely proportional to the square of the distance between them.
• Hooke's Law for elastic interactions — A mathematical approximation to the restoring behavior of springs and other elastic solids under small deformations.

Describing Interactions

Physicists have developed many ways to describe the effects of interactions. Each different description can be applied to any of the specific types of interactions listed above, with the exception that only a conservative interaction can be consistently described as a potential energy.

• Acceleration: The time rate of change of velocity of an object, or alternately the net force on the object divided by the object's mass.
• Force: Force produces a change in the momentum of a mass on which it acts, according to F=ma (Newton's Second Law). Forces result from various types of physical interactions, which always generate a pair of opposite forces acting on two different objects (Newton's Third Law).
• Impulse: The time integral of force. The net external impulse acting on a system over a given time interval is equal to the system's change in momentum.
• Work: An interaction which produces a change in the mechanical energy of a system, or the integrated scalar product of force and displacement.
• Potential Energy: A form of energy associated with the presence of conservative interactions such as gravity or a spring.
• Torque: An interaction which has the potential to produce a change in the rotational velocity of a system about a specified axis.
• Angular Impulse: the angular impulse is the integral of torque (single-axis) over the time it acts.

Classifying Interactions

Internal vs. External

For both linear and angular momentum models, interactions that take place between two system constituents will cancel from the Law of Change as a result of Newton's 3rd Law. Thus, when using a momentum or angular momentum model, it is important to classify the interactions as internal or external:

Internal Force: A force exerted on one constituent of a specified system by another constituent of the same system. Internal forces do not affect the momentum of the system's center of mass, because their effects always cancel as required by Newton's Third Law.

External Force: A force exerted on a constituent of a system by the environment.

Conservative vs. Non-Conservative

For energy models, conservative interactions should be represented by their associated potential energy, while non-conservative interactions must be accounted for as work. Thus, when using an energy model, it is important to classify the interactions as conservative or non-conservative.

Conservative Force: A force which has an associated potential energy. In introductory mechanics, the only conservative forces generally encountered are gravitation (universal) and elastic forces which satisfy Hooke's Law for elastic interactions.

Non-Conservative Force: A force which does work on an object in a path-dependent manner. For example, any force that has more than one possible value at a specific position is non-conservative.

Torque-Producing vs. Non-Torque-Producing

For angular momentum models, forces whose line of action pass directly through the chosen axis of rotation have no effect on the rotational motion of the system. Thus, when using such a model, it is important to classify the interactions as torque-producing or non-torque-producing.

Specifying Interactions in a Solution

When specifying the interactions involved as part of a problem solution, it is only necessary to focus on the interactions which are relevant to the model that you will be using. For example, if a momentum model is being used on a system consisting of more than one object, only external interactions are relevant, since internal interactions between the object in the system will cancel from the Law of Change as a result of Newton's 3rd Law. When you are specifying the interactions, you should indicate the characteristics that will lead you to choose the appropriate model (for example, if there are no external interactions, a momentum model is a good choice).