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Vector Algebra

  • A2-21: MAGNETIC VECTOR BOARD

    A2-21
    Demonstrate properties of vectors

    Various lengths of magnetic vectors can be affixed in arbitrary positions to a magnetic board. The lengths of the three longer vectors are in the ratio 3:4:5, so that they can form a right triangle. Illustrate vector addition, subtraction, motion of vectors, and commutative properties.

    Note:This board is for use in smaller classrooms; chalkboards provide magnetic base in lecture halls (Demonstration A2-22).

  • A2-22: MAGNETIC VECTORS - LECTURE HALL BLACKBOARDS

    A2-22
    Demonstration of vector properties
    Various length of magnetic vectors that can be affixed to Lecture Hall boards. The lengths are in the ratio 3:4:5, so that they can form a right triangle. Illustrate vector addition, subtraction, motion of vectors, and commutative properties. Only usable in large lecture halls with steel-backed chalkboards.
    A2

    ve

  • A2-23: VECTOR PRODUCT

    A2-23
    Illustrate the product of two vectors
    The directions of the two vectors A and B, along with their vector product AxB can be illustrated using the model. The cross product can be adjusted in length, but not reduced to zero; its minimum length is shown in the photograph above.

    This is particularly valuable for understanding concepts such as torque or the Lorentz force.
    A2

    vec

  • A2-24: TWO-DIMENSIONAL VECTOR ALGEBRA

    A2-24
    Illustrate aspects of vector algebra
    This is a projectable set of gridlines that can be used with A2-21/22 Magnetic Vectors. To provide quantitative examples, project a grid on the blackboard and read off coordinates. Demonstrate coordinate invariance by translating and rotating the grid while A+B=C is preserved by leaving the arrows fixed on the board.
    A2

  • B2-16: VECTOR ADDITION WITH ROPE AND STUDENTS

    B2-16
    Demonstrate vector addition of forces
    Two students pull the ends of the rope. A third student pulls crosswise on the center of the rope. The ends of the rope will be pulled inward by a large force, regardless of the relative size of the third student.

  • C2-24: WATER DROP PARABOLA

    C2-24
    Demonstrate the parabolic path of a projectile.
    A water stream is projected in front of a cartesian coordinate grid that can be shadow projected using a bright point source (not photographed). If desired, coordinates of the water stream can be read. The reservoir is a bottle which provides constant water pressure even as the water level drops in the container.
    C2, LS1

  • C2-41: VECTOR ADDITION OF VELOCITIES

    C2-41
    Illustrate addition of two orthogonal velocity components
    A billiard ball is placed at the corner of the apparatus. When the two mallets are pulled back and released they strike the ball simultaneously, giving it two orthogonal velocity components. The relative amount of each component is determined by how high each mallet is raised. Use the floor tiles to define your coordinates and show that equal forces in two orthogonal directions produce motion at 45 degrees with respect to the axes.
    C2

  • D1-12: ADDITION OF ANGULAR VELOCITIES

    D1-12
    Illustrate the complex motion resulting from addition of two angular velocities.
    The rotating disc with the lamp attached to its perimeter can spin in its mount on low-friction bearings. Simultaneously, the mount can be rotated by hand. As the light bulb rotates about the two axes it traces out a complicated motion which is the sum of two angular velocities.
    D1