angular momentum

(noun)

A vector quantity describing an object in circular motion; its magnitude is equal to the momentum of the particle, and the direction is perpendicular to the plane of its circular motion.

Related Terms

  • angular velocity
  • right hand rule
  • quantum mechanics
  • quantization
  • matter wave
  • torque
  • vector

Examples of angular momentum in the following topics:

  • Conservation of Angular Momentum

    • The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
    • The conserved quantity we are investigating is called angular momentum.
    • The symbol for angular momentum is the letter L.
    • If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,
    • This is an expression for the law of conservation of angular momentum.
  • Rotational Collisions

    • In a closed system, angular momentum is conserved in a similar fashion as linear momentum.
    • For objects with a rotational component, there exists angular momentum.
    • Angular momentum is defined, mathematically, as L=Iω, or L=rxp.
    • Units for linear momentum are kg⋅m/s while units for angular momentum are kg⋅m2/s.
    • An object that has a large angular velocity ω, such as a centrifuge, also has a rather large angular momentum.
  • Accretion Disks

    • The preceding section ignores an important aspect of accretion: the angular momentum of the accreta.
    • If the material starts with some net angular momentum it can only collapse so far before its angular velocity will be sufficient to halt further collapse.
    • First let's see why angular momentum can play a crucial role in accretion.
    • The initial specific angular momentum is $v b$.
    • If the material conserves angular momentum we can compare the centripetal acceleration with gravitational acceleration to give
  • Gyroscopes

    • A gyroscope is a device for measuring or maintaining orientation based on the principles of angular momentum.
    • With the wheel rotating as shown, its angular momentum is to the woman's left.
    • The torque produced is perpendicular to the angular momentum, thus the direction of the angular momentum is changed, but not its magnitude.
    • This torque causes a change in angular momentum ΔL in exactly the same direction.
    • Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces.
  • Angular Quantities as Vectors

    • The direction of angular quantities, such as angular velocity and angular momentum, is determined by using the right hand rule.
    • Angular momentum and angular velocity have both magnitude and direction and, therefore, are vector quantities.
    • The direction of angular momentum and velocity can be determined along this axis.
    • The right hand rule can be used to find the direction of both the angular momentum and the angular velocity.
    • The direction of angular velocity ω size and angular momentum L are defined to be the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disk's rotation as shown.
  • Angular Momentum Transport

    • The specific angular momentum of material in circular orbit is given by the orbital velocity times the square of the radius,
    • Because matter is falling toward the centre the angular momentum flows inward
    • The viscous stress is proportional to the viscosity and the angular velocity gradient,
  • Angular vs. Linear Quantities

    • The familiar linear vector quantities such as velocity and momentum have analogous angular quantities used to describe circular motion.
    • This type of motion has several familiar vector quantities associated with it, including linear velocity and momentum.
    • It has the same set of vector quantities associated with it, including angular velocity and angular momentum.
    • However, we can define an angular momentum vector which is constant throughout this motion.
    • The magnitude of the angular momentum is equal to the rate at which the angle of the particle advances:
  • Rotational Kinetic Energy: Work, Energy, and Power

    • where $\omega$ is the angular velocity and $I$ is the moment of inertia around the axis of rotation.
    • The instantaneous power of an angularly accelerating body is the torque times the angular velocity: $P = \tau \omega$.
    • In the rotating system, the moment of inertia takes the role of the mass and the angular velocity takes the role of the linear velocity.
    • As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10−5 rad/s.
    • Due to conservation of angular momentum this process transfers angular momentum to the Moon's orbital motion, increasing its distance from Earth and its orbital period.
  • Relationship Between Torque and Angular Acceleration

    • Torque is equal to the moment of inertia times the angular acceleration.
    • Torque and angular acceleration are related by the following formula where is the objects moment of inertia and $\alpha$ is the angular acceleration .
    • Similar to Newton's Second Law, angular motion also obeys Newton's First Law.
    • Relationship between force (F), torque (τ), momentum (p), and angular momentum (L) vectors in a rotating system
    • Torque, Angular Acceleration, and the Role of the Church in the French Revolution
  • Relationship Between Linear and Rotational Quantitues

    • The description of motion could be sometimes easier with angular quantities such as angular velocity, rotational inertia, torque, etc.
    • The velocity (i.e. angular velocity) is indeed constant.
    • This is the first advantage of describing uniform circular motion in terms of angular velocity.
    • As we use mass, linear momentum, translational kinetic energy, and Newton's 2nd law to describe linear motion, we can describe a general rotational motion using corresponding scalar/vector/tensor quantities:
    • For the description of the motion, angular quantities are the better choice.
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