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An extended object in which the distance between any two points in the object is constant in time.  

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h2.  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.


h2. Effects of External Forces on Rigid Bodies

h3. 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|Newton's Second Law] applied to the entire body:

{latex}\begin{large}\[ \sum \vec{F}_{\rm ext} = MaM\vec{a}\] \end{large}{latex}

where _M_ is the mass of the entire body.

h3.  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|torque] 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:

{latex}\begin{large}\[ \sum \tau = I\alpha \]\end{large}{latex}

where _I_ is the [moment of inertia] of the body about the axis of the resulting rotation.

{latex}\begin{large}

h3.  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.


h2. Relevant Models



h2. Relevant Examples