Catalog of Sites and Images

Lecture: Vectors

Don't Panic

The sites/images are mainly those of/from Wikipedia.

Sections

  1. Alphabetic Listing
  2. Lecture Listing

  1. Alphabetic Listing

    1. Images.

    2. acceleration Images.

    3. angular momentum Images and animations. The animation is good.

    4. displacement Images.

    5. momentum Images. Nothing real exciting though.

    6. scalar in phyiscs No images.

    7. torque Images.

    8. vectors in general No images.

    9. vectors in geometry Images. Nothing real exciting though.

    10. vector field Images.

    11. velocity No images.

  2. Lecture Listing

    1. scalar in phyiscs No images. A scalar is a quantity with only a magnitude.

    2. vectors in geometry Images. A scalar is a quantity with a magnitude and a direction in space space, but it only has an extend in space space if it is the displacement vector.

    3. displacement Images.

        Displacement is a distance with a direction.

        Distance is the magnitude of displacement or the length of any path curved or straight.

        Displacement is the prototype vector in fact.

        All other things which are called vectors must have the transformation properties of displacment in order to be vectors.

        The transformations are the transformations of the coordinate systems---a subject which is beyond our scope.

    4. velocity No images.

        Velocity is the rate of change of displacement.

    5. acceleration Images.

        Acceleration is the rate of change of velocity

        Graphically, acceleration is the slope of a velocity curve for 1-dimensional motion.

    6. momentum Images. Nothing real exciting though.

        Momentum is mass times velocity.

        This turns out to be a useful quantity in physics.

    7. angular momentum Images and animations. The animation is good.

        Angular momentum is another vector quantity that turns out to be useful in physics.

        It is the rotational analog of momentum.

        It's defined (vec L)=(vec r) x (vec p), where (vec L) is the angular momentum, (vec r) is the displacement vector from some origin, (vec p) is momentum and the operation is the cross product---which is a very angry kind of product.

        It's actually a pseudovector, but we won't go into all that.

        For a particle in simple rotation about an axis in a circle, angular momentum is L=mvr, where m is mass, v is speed, r is radius from the axis, and the vector direction is along the axis of rotation in a sense given by a right-hand rule: curl the fingers of your right-hand in the direction of rotation and your thumb gives the sense.

    8. torque Images.

        Then there is torque---not to be confused with Tork or tuque.

        It is the rotational analog of force.

        It's defined (vec tau)=(vec r) x (vec F), where (vec tau) is torque, (vec r) is the displacement vector from some origin, (vec F) is force and the operation is the cross product---which is a very angry kind of product.

        It's actually a pseudovector, but we won't go into all that.

    9. vector field Images.

        A vector field is vector quantity defined at every point in space.

        Illustration usually show a finite number of arrows representing vectors. The arrow ends are usually at the point where the vector is evaluated.

        The vectors form a continuum, and so any illustration is just schematic.

        The flow field or velocity field of a fluid in motion is an example of a vector field. Every point in a fluid flow has a velocity: those velocity vectors constitute a vector field.

        The electric field, magnetic field, and gravitational field well known physical fields. They are the immediate causes, respectively, of the electric, magnetic, and gravitational forces.