An extended object in which the distance between any two points in the object is constant in time.
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Motivation of Concept
Many everyday objects are essentially rigid bodies. Any object which does not significantly deform in its everyday use can be treated as a rigid body. Some examples are ceramic cups, keys, wooden chairs, and hockey pucks.
These objects should be contrasted with other objects that significantly deform when forces are applied. Examples are handbags, unrolled newspapers, cords, and beanbags.
Effects of External Forces on Rigid Bodies
Pure Translational Acceleration
Forces applied to a rigid body in such a way that their line of action passes through the body's center of mass will produce pure translation of the rigid body. The acceleration of every point in the rigid body will be identical and governed by Newton's 2nd Law applied to the entire body:
\begin
[ \sum \vec{F]_
= Ma] \end
where M is the mass of the entire body.
Pure Rotation
Even in the case that all external forces sum to zero, an extended rigid body may experience a change in its state of motion. If the [torques] resulting from the applied forces do not sum to zero, the rigid body will experience an angular acceleration about its center of mass, changing its rotational state. Assuming that the body possesses certain [rotational symmetries], the angular acceleration of every point in the body will be identical and will be governed by the formula:
\begin
[ \sum \tau = I\alpha ]\end
where I is the moment of inertia of the body about the axis of the resulting rotation.
\begin
Combined Rotation and Translation
If neither the forces nor the torques sum to zero, the motion of the rigid body can be treated as the sum of the resulting translational acceleration and rotational acceleration found by the methods described in the previous sections.