kinetic energy

Examples of kinetic energy 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.
  • The earth's rotation is a prominent example of rotational kinetic energy.
  • 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

• 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:
  • At a low speed ($v << c$), the relativistic kinetic energy may be approximated well by the classical kinetic energy.
  • Thus, the total energy can be partitioned into the energy of the rest mass plus the traditional classical kinetic energy at low speeds.

• 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.
  • 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.
  • 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.

• 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.
  • If two objects collide, there are many ways that kinetic energy can be transformed into other forms of energy.
  • For example, in the collision of macroscopic bodies, some kinetic energy is turned into vibrational energy of the constituent atoms.
  • Another example in which kinetic energy is transformed into another form of energy is when the molecules of a gas or liquid collide.
  • The kinetic energy is used on the bonding energy of the two bodies.

• Internal Energy of an Ideal Gas

  • Internal energy is the total energy contained by a thermodynamic system, and has two major components: kinetic energy and potential energy.
  • Internal energy has two major components: kinetic energy and potential energy.
  • 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:

• Overview of Temperature and Kinetic Theory

  • 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:
  • 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.
  • 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:

• 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

• Problem Solving With the Conservation of Energy

  • When they start rising, the kinetic energy begins to be converted to gravitational potential energy ($PE_g$).
  • The sum of kinetic and potential energy in the system should remain constant, if losses to friction are ignored .
  • The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path.
  • When they start rising, the kinetic energy begins to be converted to gravitational potential energy.
  • The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.

• Other Forms of Energy

  • Electric Energy: This is energy that is from electrical potential energy, a result of Coulombic forces.
  • It is the sum of all of the kinetic and potential energy that the object has.
  • In each of the aforementioned forms, energy exists as either kinetic energy, potential energy, or a combination of both.
  • For example, luminous energy is radiant energy.
  • A brief overview of energy, kinetic energy, gravitational potential energy, and the work-energy theorem for algebra-based physics students.