GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 61–90 of 1709 reference entries

Physics · MeasurementElectric current

Current measures charge crossing a chosen surface per unit time.

DefinitionPhysicsElectric field and force

An electric field assigns force per unit test charge.

DefinitionPhysicsMagnetic force on a moving charge

Magnetic force depends on charge motion relative to the field.

ModelPhysicsOhm's law and its domain

A linear current-voltage relation requires suitable conditions.

Empirical findingPhysicsFirst law of thermodynamics

Keep the heat and work sign convention explicit in an energy balance.

ModelPhysicsSecond law: isolated-system entropy

Apply entropy increase to the whole isolated system.

ModelPhysics · ChemistryIdeal-gas equation of state

A simple gas model relates pressure, amount, volume and temperature.

ModelPhysicsPhoton energy and frequency

One photon's energy is proportional to its frequency.

ModelPhysics · Mathematics & logicInvariant spacetime interval

Lorentz transformations preserve a combined space-time separation.

ModelPhysicsNewton's third law

Interaction forces act on different bodies in equal and opposite pairs.

ModelPhysicsAngular momentum and torque

Torque changes angular momentum about a specified origin.

ModelPhysicsHydrostatic pressure

Static fluid pressure rises with depth under gravity.

ModelPhysicsArchimedes' buoyancy principle

The hydrostatic upward force equals displaced-fluid weight.

ModelPhysicsMaxwell equations in free space

Four field equations connect electric and magnetic fields with charge and current.

ModelPhysicsSchrödinger time evolution

A quantum wavefunction evolves according to its Hamiltonian.

ModelPhysicsBorn position probability

A normalized wavefunction assigns probabilities to position intervals.

ModelPhysics · MeasurementElementary charge

The elementary charge has an exact SI numerical value.

DefinitionPhysics · MeasurementBoltzmann constant

The Boltzmann constant has an exact SI numerical value.

DefinitionMeasurement · Chemistry · PhysicsAvogadro constant

The mole is linked to a specified number of entities.

DefinitionMeasurement · PhysicsSI defining luminous efficacy

A specified frequency fixes the photometric SI reference.

DefinitionChemistryAtoms and elemental identity

The proton count of an atomic nucleus identifies its chemical element.

DefinitionChemistryIsotopes and mass number

Isotopes share a proton count but have different neutron counts.

DefinitionChemistryPeriodic organization of the elements

Atomic-number order reveals recurring patterns in electron structure and chemical properties.

ModelChemistryChemical bonds

Bonding describes interactions that bind atoms into molecules or extended structures.

DefinitionChemistry · MeasurementMole and amount of substance

The mole counts specified entities using the exact Avogadro constant.

DefinitionChemistryReaction stoichiometry

Balanced coefficients relate the amounts consumed and produced by a reaction.

MethodChemistryBalancing atoms and electric charge

A chemical equation must preserve each element's atom count and the total charge.

MethodChemistryDynamic chemical equilibrium

At equilibrium, opposing reactions continue without net composition change.

ModelChemistryBrønsted acids and bases

In the Brønsted description, an acid donates a proton and a base accepts it.

DefinitionChemistryGibbs energy and thermodynamic direction

Gibbs-energy change distinguishes thermodynamic favourability from reaction speed.

Model
ModelSource checked

Angular momentum and torque

Physics

Torque changes angular momentum about a specified origin.

Key knowledge

For a constant-mass Newtonian particle about a fixed inertial origin, angular momentum is L = r × p and its time derivative equals net torque τ_net = r × F_net. Zero net torque about that origin therefore preserves L.

Values and equations

L = r × p; τ_net = r × F_net; dL/dt = τ_net

L
Particle angular-momentum vector about the chosen origin kg m² s⁻¹
r
Position vector from the fixed origin m
p
Particle linear momentum in the inertial frame kg m s⁻¹
τ_net
Net torque vector about that origin N m
F_net
Net force on the particle N
t
Time s

Conditions and scope

  • The origin is fixed in an inertial frame, with r measured from it and p = mv in that frame.
  • All forces on the particle are included; a moving origin requires additional terms.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics, volume 1: Angular MomentumSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
  2. System of Particles and Rotational Motion · Physics (2026–27 reprint)National Council of Educational Research and Training (NCERT)Textbook chapter · PDFncert.nic.inRead source

Evidence and review

OpenStax 11.2, equations 11.5–11.6: particle definition and derivative using Newton's second law.

2026-10-10 · Particle angular momentum, torque and zero-torque consequence only; arbitrary rigid-body rotation is not summarized by a scalar L = Iω here.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Agreement within this scope

For a particle about a fixed origin, angular momentum is r×p and its time derivative is torque r×F.

Moving origins require additional terms; the fixed inertial-origin domain is retained.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–6 of 6 relationships

Scientific relationships · 6 / 6

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Derived from
    Relationship sources · 1

    For a particle about a fixed inertial origin, differentiating r × p and applying Newton's second law gives net torque.

  2. Uses definition
    Relationship sources · 2

    Linked statements

    • For a rigid body, the inertia tensor about its centre of mass gives rotational angular momentum L = Iω. Its diagonal entries measure squared distances from axes; off-diagonal matrix entries carry minus coordinate products.

    Rigid-body rotational angular momentum about its centre of mass.

  3. Related to
    Relationship sources · 1

    Linked statements

    • Neutron-star pulsars have rotating magnetized stellar remnants whose emission can sweep past the observer. For a rotation-powered model with constant moment of inertia I, E_rot=IΩ²/2=2π²I/P² and rotational energy loss is −dE_rot/dt=4π²IṖ/P³. This inferred power is distinct from luminosity measured in one observing band. Under constant PṖ and negligible initial period, the characteristic age is τ_c=P/(2Ṗ).

    Rotation and changing torque connect to angular momentum.

  4. Related to
    Relationship sources · 2

    Linked statements

    • Matter moving inward in a gravitational field can release binding energy if energy is dissipated. For matter initially nearly at rest far from a Newtonian object of mass M and material radius R, available gravitational power scales as GMṀ/R. A radiated accretion luminosity is often parameterized L_acc=ηṀc² using an explicitly defined inflow rate and radiative efficiency. In a rotating disk, stress transports angular momentum so material can move inward; inflow and radiation need not have a universal efficiency.

    Disk inflow requires angular-momentum transport.

  5. Related to
    Relationship sources · 2

    Linked statements

    • A free-body diagram represents all external forces acting on the selected body or system. Forces the system exerts on its surroundings belong on another system’s diagram. A force and its components are alternative representations, and the net force is their sum rather than an extra force. For an extended body, force locations are also needed to determine torque.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  6. Related to
    Relationship sources · 1

    Linked statements

    • A rigid body initially at rest in an inertial frame remains in static equilibrium when both net external force and net external torque vanish. Torque must include lever arms and applied couples. Once net force is zero, changing the torque origin does not change the net torque; a pair of opposite forces at different locations can still create a couple.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

Entry detailsPermanent link to this entry ↗
Record identity
physics-angular-momentum
Revision
core.1
Structured reference record
Essential core · first collection · University core expansion