translation

Examples of translation in the following topics:

• Center of Mass and Translational Motion

  • While translating in the air, the stick rotates about a moving axis, as shown in .
  • We describe the translational motion of a rigid body as if it is a point particle with mass m located at COM.
  • We "separate" the translational part of the motion from the rotational part.
  • By introducing the concept of COM, the translational motion becomes that of a point particle with mass m.

• Conservation of Energy in Rotational Motion

  • Energy is conserved in rotational motion just as in translational motion.
  • Work and energy in rotational motion are completely analogous to work and energy in translational motion and completely transferrable.
  • Just as in translational motion (where kinetic energy equals 1/2mv2 where m is mass and v is velocity), energy is conserved in rotational motion.

• Rolling Without Slipping

  • The motion of rolling without slipping can be broken down into rotational and translational motion.
  • Rolling without slipping can be better understood by breaking it down into two different motions: 1) Motion of the center of mass, with linear velocity v (translational motion); and 2) rotational motion around its center, with angular velocity w.

• Overview of Temperature and Kinetic Theory

  • The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium .
  • Classical mechanics defines the translational kinetic energy of a gas molecule as follows:
  • The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classical ideal gas is called the Maxwell-Boltzmann distribution.

• Internal Energy of an Ideal Gas

  • ., translations, rotations, vibrations).
  • In this case, the kinetic energy consists only of the translational energy of the individual atoms.
  • Therefore, practical internal energy changes in an ideal gas may be described solely by changes in its translational kinetic energy.
  • Note that there are three degrees of freedom in monatomic gases: translation in x, y and z directions.
  • A diatomic molecule (H2, O2, N2, etc.) has 5 degrees of freedom (3 for translation in x, y and z directions, and 2 for rotation).

• Rotational Kinetic Energy: Work, Energy, and Power

  • Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:
  • Things that roll without slipping have some fraction of their energy as translational kinetic and the remainder as rotational kinetic.

• Relationship Between Torque and Angular Acceleration

  • From a translational viewpoint, at least, there would be no net force applied to the turntable.
  • Therefore, the turntable would be in translational equilibrium.
  • From this we might conclude that just because a rotating object is in translational equilibrium, it is not necessarily in rotational equilibrium.

• Translational Equilibrium

  • Static or dynamic, these kinds of equilibrium can be categorized as translational equilibrium.
  • Examples of translational equilibrium are all around us.

• 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 COM—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).
  • Derive the center of mass for the translational motion of a rigid body

• Temperature

  • Temperature is directly proportional to the average translational kinetic energy of molecules in an ideal gas.
  • We can derive a relationship between temperature and the average translational kinetic energy of molecules in a gas.
  • The average translational kinetic energy of a molecule is called thermal energy.