tangent

Examples of tangent in the following topics:

• Instananeous Velocity: A Graphical Interpretation

  • Instantaneous velocity is the velocity of an object at a single point in time and space as calculated by the slope of the tangent line.
  • That line would be the line tangent to the curve at that point.
  • The velocity of an object at any given moment is the slope of the tangent line through the relevant point on its x vs. t graph.
  • The velocity at any given moment is defined as the slope of the tangent line through the relevant point on the graph

• Angular Acceleration, Alpha

  • In circular motion, there is acceleration that is tangent to the circle at the point of interest (as seen in the diagram below).
  • In circular motion, acceleration can occur as the magnitude of the velocity changes: a is tangent to the motion.

• Huygens' Principle

  • The new wavefront is a line tangent to all of the wavelets.
  • The new wavefront is tangent to the wavelets.
  • The tangent to these wavelets shows that the new wavefront has been reflected at an angle equal to the incident angle.
  • The new wavefront is a line tangent to the wavelets.

• Electric Field Lines: Multiple Charges

  • It should also be noted that at any point, the direction of the electric field will be tangent to the field line.
  • Thus, given charges q1, q2 ,... qn, one can find their resultant force on a test charge at a certain point using vector addition: adding the component vectors in each direction and using the inverse tangent function to solve for the angle of the resultant relative to a given axis.

• Spectrum of Synchrotron radiation

  • We know that the electric field vanishes everywhere except within a cone of opening angle $1/\gamma$, so a distance observer will only detect a significant electric field while the electron is within an angle $\Delta \theta/2 \sim 1/\gamma$of the point where the path is tangent to the line of sight.

• Non-relativistic Shocks

  • Furthermore, we can see that the curves of constant entropy not only pass through the corresponding plots in the plane (this is by design) but they are also tangent to and have the same radius of curvature as the shock adiabats.
  • so the Mach numbers on each side of the shock are given by the ratio of the slope of the secant to the slope of the tangent.
  • Because all of the adiabats are concave up in the $p-V-$plane, the slope of the secant must be larger than that of the tangent at $(p_1,V_1)$, so the flow enters the shock supersonically.
  • Conversely at $(p_2,V_2)$the slope of the secant must be small than that of the tangent, so the flow exits the shock subsonically.

• Superposition of Fields

  • An overall resultant vector can be found by using the Pythagorean theorem to find the resultant (the hypotenuse of the triangle created with applied forces as legs) and the angle with respect to a given axis by equating the inverse tangent of the angle to the ratio of the forces of the adjacent and opposite legs.

• Simple Harmonic Motion and Uniform Circular Motion

  • Since velocity v is tangent to the circular path, no two velocities point in the same direction.
  • Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangent to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation

• The Simple Pendulum

  • We see from the figure that the net force on the bob is tangent to the arc and equals −mgsinθ.
  • (The weight mg has components mgcosθ along the string and mgsinθ tangent to the arc. ) Tension in the string exactly cancels the component mgcosθ parallel to the string.

• Electric vs. Magnetic Forces

  • A consequence of this is that the electric field may do work and a charge in a pure electric field will follow the tangent of an electric field line.
  • The electric field is directed tangent to the field lines.