pivot

(noun)

Moving from one basic feasible solution to an adjacent basic feasible solution.

Related Terms

Examples of pivot in the following topics:

  • The Physical Pendulum

    • Recall that a simple pendulum consists of a mass suspended from a massless string or rod on a frictionless pivot.
    • In this case, the pendulum's period depends on its moment of inertia around the pivot point .
    • where h is the distance from the center of mass to the pivot point and θ is the angle from the vertical.
    • For illustration, let us consider a uniform rigid rod, pivoted from a frame as shown (see ).
    • A rigid rod with uniform mass distribution hangs from a pivot point.

  • Lever Systems

    • If a load is close to a pivot and the force is applied far from the pivot, then the lever is said to operate at mechanical advantage.
    • If a load is far from a pivot and a force is applied near to the pivot, then the lever is said to operate at a mechanical disadvantage.
    • In muscles, the joints are the pivots and the bones are the fixed rods.
    • In a first class lever, the load and force sit on either side of the pivot like a seesaw.
    • In a third-class lever the force is applied between the load and the pivot.

  • Application of Systems of Inequalities: Linear Programming

    • Now, the Simplex Method proceeds by performing successive pivot operations which each improve the basic feasible solution; the choice of pivot element at each step is largely determined by the requirement that this pivot improves the solution.
    • For the choice of pivot row, only positive entries in the pivot column are considered.
    • If the pivot column is c, then the pivot row r is chosen so that $b_{r}/a_{cr}$ is at a minimum.
    • Of these, the minimum is 5, so row 3 must be the pivot row.
    • Performing the pivot produces:

  • Modulation

    • A pivot-chord modulation makes use of at least one chord that is native to both the old key and the new key.
    • The smoothest type of pivot-chord modulation uses a pivot-chord that expresses the same function in both keys, preferably subdominant function, but other functional arrangements are possible and commonly used.
    • A pivot-chord modulation is notated in a special way.
    • The pivot chord receives its analytical symbol for the old key, as usual.
    • Below that symbol is the new key, colon, and the analytical symbol for the pivot chord in the new key.

  • Internal Expansions

    • A pivot-chord modulation makes use of at least one chord that is native to both the old key and the new key.
    • The smoothest type of pivot-chord modulation uses a pivot-chord that expresses the same function in both keys, preferably subdominant function, but other functional arrangements are possible and commonly used.
    • A pivot-chord modulation is notated in a special way.
    • The pivot chord receives its analytical symbol for the old key, as usual.
    • Below that symbol is the new key, colon, and the analytical symbol for the pivot chord in the new key.

  • Types of Synovial Joints

    • The types of the synovial joints are based on the shapes and can be classified as plane, hinge, pivot, condyloid, saddle, and ball and socket.
    • In a pivot joint the rounded end of the bone fits into a sleeve or ring of bone.
    • The atlanto-axial joint, proximal radioulnar joint, and distal radioulnar joint are examples of pivot joints.
    • Collection of Joint Movements (Example): Wave your arm (hinge joint) and hand (condyloid joint) while nodding your head (pivot joint), and giving a thumbs up (saddle joint).

  • Types of Synovial Joints

    • Synovial joints include planar, hinge, pivot, condyloid, saddle, and ball-and-socket joints, which allow varying types of movement.
    • These joints can be described as planar, hinge, pivot, condyloid, saddle, or ball-and-socket joints .
    • Pivot joints consist of the rounded end of one bone fitting into a ring formed by the other bone.
    • An example of a pivot joint is the joint of the first and second vertebrae of the neck that allows the head to move back and forth .
    • The joint of the wrist that allows the palm of the hand to be turned up and down is also a pivot joint.

  • Problem-Solving Techniques

    • There is enough information to use the second condition for equilibrium (τnet = 0) if the pivot point is chosen to be at either hand, making the torque at that hand zero.
    • We choose to locate the pivot at the left hand in this part of the problem to eliminate the torque from the left hand.Solution for (a)There are now only two nonzero torques: that from the gravitational force (τw) and that from the push or pull of the right hand (τR).
    • Choose a pivot point.
    • If the choice is not obvious, pick the pivot point as the location at which you have the most unknowns .
    • This simplifies things because forces at the pivot point create no torque because of the cross product: $\tau = rF$

  • Simple Machines

    • They use only three forces: the input force, output force, and force on the pivot.
    • In the case of wheelbarrows, the output force is between the pivot (wheel's axle) and the input force.
    • In the shovel, the input force is between the pivot and the load.

  • Second Condition

    • In equation form, the magnitude of torque is defined to be τ=rFsinθ where τ (the Greek letter tau) is the symbol for torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the vector directed from the point of application to the pivot point.