kinetic

Examples of kinetic in the following topics:

• Rotational Kinetic Energy: Work, Energy, and Power

  • The rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.
  • Rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy .
  • Therefore, it has a rotational kinetic energy of 2.138×1029 J.
  • Things that roll without slipping have some fraction of their energy as translational kinetic and the remainder as rotational kinetic.
  • Express the rotational kinetic energy as a function of the angular velocity and the moment of inertia, and relate it to the total kinetic energy

• Overview of Temperature and Kinetic Theory

  • The kinetic theory of gases describes a gas as a large number of small particles (atoms and molecules) in constant, random motion.
  • Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .
  • 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:
  • In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:

• Relativistic Kinetic Energy

  • The classical kinetic energy of an object is related to its momentum by the equation:
  • Since the kinetic energy of an object is related to its momentum, we intuitively know that the relativistic expression for kinetic energy will also be different from its classical counterpart.
  • Indeed, the relativistic expression for kinetic energy is:
  • The general expression for the kinetic energy of an object that is not at rest is:
  • At a low speed ($v << c$), the relativistic kinetic energy may be approximated well by the classical kinetic energy.

• Kinetic Energy and Work-Energy Theorem

  • The work-energy theorem states that the work done by all forces acting on a particle equals the change in the particle's kinetic energy.
  • The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
  • This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
  • The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
  • The kinetic energy of the block increases as a result by the amount of work.

• Conservation of Energy in Rotational Motion

  • This work went into heat, light, sound, vibration, and considerable rotational kinetic energy.
  • Kinetic energy (K.E.) in rotational motion is related to moment of rotational inertia (I) and angular velocity (ω):
  • The final rotational kinetic energy equals the work done by the torque:
  • This confirms that the work done went into rotational kinetic energy.
  • The motor works in spinning the grindstone, giving it rotational kinetic energy.

• Friction: Kinetic

  • If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction.
  • When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat.
  • Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred.
  • Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together; a sled on the ground would be a good example of kinetic friction.
  • The coefficient of kinetic friction is typically represented as $\mu_k$ and is usually less than the coefficient of static friction for the same materials.

• Inelastic Collisions in One Dimension

  • In an inelastic collision the total kinetic energy after the collision is not equal to the total kinetic energy before the collision.
  • This is in contrast to an elastic collision in which conservation of total kinetic energy applies.
  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum.
  • A perfectly inelastic collision happens when the maximum amount of kinetic energy in a system is lost.
  • The kinetic energy is used on the bonding energy of the two bodies.

• Internal Energy

  • The internal energy of a system is the sum of all kinetic and potential energy in a system.
  • Internal energy has two components: kinetic energy and potential energy.
  • The kinetic energy consists of all the energy involving the motions of the particles constituting the system, including translation, vibration, and rotation.
  • The kinetic energy portion of internal energy gives rise to the temperature of the system.
  • Express the internal energy in terms of kinetic and potential energy

• Internal Energy of an Ideal Gas

  • Internal energy has two major components: kinetic energy and potential energy.
  • The kinetic energy is due to the motion of the system's particles (e.g., translations, rotations, vibrations).
  • Therefore, we will disregard potential energy and only focus on the kinetic energy contribution to the internal energy.
  • In this case, the kinetic energy consists only of the translational energy of the individual atoms.
  • The average kinetic energy (KE) of a particle in an ideal gas is given as:

• Inelastic Collisions in Multiple Dimensions

  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum.
  • It is still true that the total kinetic energy after the collision is not equal to the total kinetic energy before the collision.
  • While inelastic collisions may not conserve total kinetic energy, they do conserve total momentum .
  • We can now calculate the initial and final kinetic energy of the system to see if it the same.