rigid body

(noun)

Definition of rigid body

An idealized solid whose size and shape are fixed and remain unaltered when forces are applied; used in Newtonian mechanics to model real objects.

Source: Wiktionary - CC BY-SA 3.0

Examples of rigid body in the following topics:

• Motion of the Center of Mass

• We can describe the translational motion of a rigid body as if it is a point particle with the total mass located at the center of mass (COM).
• We can describe the translational motion of a rigid body as if it is a point particle with the total mass located at the COM—center of mass.
• The Physical Pendulum

• In contrast, a physical pendulum (sometimes called a compound pendulum) may be suspended by a rod that is not massless or, more generally, may be an arbitrarily-shaped, rigid body swinging by a pivot (see ).
• Gravity acts through the center of mass of the rigid body.
• For illustration, let us consider a uniform rigid rod, pivoted from a frame as shown (see ).
• Clearly, the center of mass is at a distance L/2 from the point of suspension: $h=\frac{L}{2}$.The moment of inertia of the rigid rod about its center is:$I_{c}=\frac{mL^{2}}{12}$.However, we need to evaluate the moment of inertia about the pivot point, not the center of mass, so we apply the parallel axis theorem:$I_{o}=I_{c}+mh^{2}=\frac{mL^{2}}{12}+m(\frac{L}{2})^{2}=\frac{mL^{2}}{3}$.Plugging this result into the equation for period, we have:$T=2\pi \sqrt{\frac{I}{mgh}}=2\pi\sqrt{\frac{2mL^{2}}{3mgL}}=2\pi\sqrt{\frac{2L}{3g}}$.The important thing to note about this relation is that the period is still independent of the mass of the rigid body.
• However, it is not independent of the mass distribution of the rigid body.
• Center of Mass and Translational Motion

• We have referred to particle, object and body in the same way.
• By doing this, we have essentially considered a rigid body as a point particle.
• Center of Mass (COM) An actual body, however, can move differently than this simplified paradigm.
• Different parts of a body have different motions.
• Describing Motion in a Rigid Body We can describe general motion of an object (with mass m) as follows: We describe the translational motion of a rigid body as if it is a point particle with mass m located at COM.
• General Problem-Solving Tricks

• A force on a particle is a bound vector. rigid extended.
• A force on an extended rigid body is asliding vector. non-rigid extended.
• A force on a non-rigid body is a bound vector.
• So you will want to include the following things in the diagram: The body: This is usually sketched in a schematic way depending on the body - particle/extended, rigid/non-rigid - and on what questions are to be answered.
• Internal forces acting on various parts of the body by other parts of the body.
• Free body diagrams use geometry and vectors to visually represent the problem.
• Locating the Center of Mass

• In the previous atom on "Center of Mass and Translational Motion," we learned why the concept of center of mass (COM) helps solving mechanics problems involving a rigid body.
•  If a continuous mass distribution has uniform density, which means ρ is constant, then the center of mass is the same as the center of the volume.Locating the Center of MassThe experimental determination of the center of mass of a body uses gravity forces on the body and relies on the fact that in the parallel gravity field near the surface of Earth the center of mass is the same as the center of gravity.The center of mass of a body with an axis of symmetry and constant density must lie on this axis.
• In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere.
• In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry.In two dimensions: An experimental method for locating the center of mass is to suspend the object from two locations and to drop plumb lines from the suspension points.
• Stability, Balance, and Center of Mass

• To quantify equilibrium for a single object, there are two conditions:The net external force on the object is zero: $\sum_i \mathbf{F}_i = \mathbf{F}_{net} = 0$The net external torque, regardless of choice of origin, is also zero : $\sum_i \mathbf{r}_i \times \mathbf{F}_i = \sum_i \mathbf{\tau}_i = \mathbf{\tau}_{net} = 0$Those two conditions hold regardless of whether the object we are talking about is a single point particle, a rigid body, or a collection of discrete particles.