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In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid [1].Some authors exclude uniform polyhedra (in which all vertices are symmetric to each other) from the definition; uniform polyhedra include Platonic and Archimedean solids as well as prisms and antiprisms. [2]
a point such that the translational motion is zero or simplified, e.g. on an axle or hinge, at the center of a ball and socket joint, etc. When the center of mass is used as reference point: The (linear) momentum is independent of the rotational motion. At any time it is equal to the total mass of the rigid body times the translational velocity.
At equilibrium, the center of mass and the contact point are on the line perpendicular to the ground. When the toy is pushed, its center of mass rises and shifts away from that line. This produces a righting moment, which returns the toy to its equilibrium position. The above examples of mono-monostatic objects are inhomogeneous.
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. The intersection of the two lines is the center of mass. [17] The shape of an object might already be mathematically determined, but it may be too complex to use a known formula.
Using the center of mass and inertia matrix, the force and torque equations for a single rigid body take the form =, = [] + [], and are known as Newton's second law of motion for a rigid body. The dynamics of an interconnected system of rigid bodies, B i , j = 1, ..., M , is formulated by isolating each rigid body and introducing the ...
The total center of mass of the forks, cork, and toothpick is on top of the pen's tip. Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed.
If one object is very much heavier than the other, it will move far less than the other with reference to the shared center of mass. The mutual center of mass may even be inside the larger object. For the derivation of the solutions to the problem, see Classical central-force problem or Kepler problem .
Balloon skewer experiment. A pin or needle is frequently used to pop a balloon. [4] As the needle or pin creates a hole on the balloon surface, the balloon pops. However, if tape is placed on the part where the hole is created, the balloon will not pop since the tape helps reinforce the elastic tension in that area, preventing the edges of the hole pulling away from the center. [5]