radial

Examples of radial in the following topics:

• Overview of Non-Uniform Circular Motion

  • The change in speed has implications for radial (centripetal) acceleration.
  • A change in $v$ will change the magnitude of radial acceleration.
  • The greater the speed, the greater the radial acceleration.
  • 2: The radial (centripetal) force is constant (like a satellite rotating about the earth under the influence of a constant force of gravity).
  • The important thing to note here is that, although change in speed of the particle affects radial acceleration, the change in speed is not affected by radial or centripetal force.

• Stress and Strain

  • If the charge is positive, field lines point radially away from it; if the charge is negative, field lines point radially towards it.
  • The above equation is defined in radial coordinates which can be seen in .
  • The electric field of a positively charged particle points radially away from the charge.
  • The electric field of a negatively charged particle points radially toward the particle.
  • The electric field of a point charge is defined in radial coordinates.

• Electric Field from a Point Charge

  • If the charge is positive, field lines point radially away from it; if the charge is negative, field lines point radially towards it .
  • The above equation is defined in radial coordinates, which can be seen in .
  • The electric field of a positively charged particle points radially away from the charge.
  • The electric field of a negatively charged particle points radially toward the particle.
  • The electric field of a point charge is defined in radial coordinates.

• A single electron in a central field

  • If the potential is a function of the radial distance from the nucleus alone the Schrodinger equation is separable,
  • $V(r)$ is the radial potential and the term proportional to $l(l+1)$ is the centripetal potential.
  • Because the equation does not depend on $m$, the radial wavefunction only depends on $l$.
  • Because the radial eigenfunctions for different values of $l$ satisfy different equations, there is no orthogonality relation for the radial wavefunctions with different $l$ values.

• Equipotential Lines

  • Since they are located radially around a charged body, they are perpendicular to electric field lines, which extend radially from the center of a charged body.
  • For a single, isolated point charge, the formula for potential (V) is functionally dependent upon charge (Q) and inversely dependent upon radial distance from the charge (r):
  • The radial dependence means that at any point a certain distance from the point charge, potential will be the same.

• Rotational Collisions

  • If the archer releases the arrow with a velocity v1i and the arrow hits the cylinder at its radial edge, what's the final momentum ?
  • Initially, the cylinder is stationary, so it has no momentum linearly or radially.

• Circular Motion

  • The perpendicular direction to the circular trajectory is, therefore, the radial direction.
  • Therefore, the force (and therefore the acceleration) in uniform direction motion is in the radial direction.

• Kinematics of UCM

  • Any force or combination of forces can cause a centripetal or radial acceleration.

• Exercises

  • It is easy to show, similarly to what we did with the axi-symmetric spherical harmonics, that in the case $k=0$, the radial solutions are of the form $r^m$ and $r^{-m}$ (for $m> 0$).
  • To see this just make a trial solution of the form $R(r) = Ar^\alpha$, then show that this satisfies the radial equation if and only if $\alpha^2 = m^2$.
  • The radial equation above is almost in the standard form of Bessel's equation.
  • and we would have gotten $Z$ solutions proportional to $e^{\pm i k z}$ and the radial equation would have been:

• Spherical Distribution of Charge

  • For a positive charge, the direction of the electric field points along lines directed radially away from the location of the point charge, while the direction is towards for a negative charge.