radius

Examples of radius in the following topics:

• Ulna and Radius (The Forearm)

  • Anatomically, the ulna is located medially to the radius, placing it near the little finger.
  • The ulna is slightly larger than the radius.
  • Anatomically, the radius is located laterally to the ulna placing it near the thumb.
  • Distally the radius expands, medially the ulnar notch articulates with the head of the ulnar.
  • Immediately adjacent to the ulnar notch, the radius articulates with the scaphoid and lunate carpal bones to form part of the wrist.

• Atomic Radius

  • The atomic radius is one such characteristic that trends across a period and down a group of the periodic table.
  • Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius.
  • The value of an atomic radius may be obtained through experimental measurements or computed with theoretical models.
  • Under some definitions, the value of a radius may depend on the atom's state and context.
  • A chart showing the atomic radius relative to the atomic number of the elements.

• Radians

  • If we divide both sides of this equation by $r$, we create the ratio of the circumference, which is always $2\pi$ to the radius, regardless of the length of the radius.
  • So the circumference of any circle is $2\pi \approx 6.28$ times the length of the radius.
  • Just as the full circumference of a circle always has a constant ratio to the radius, the arc length produced by any given angle also has a constant relation to the radius, regardless of the length of the radius.
  • (a) In an angle of 1 radian; the arc lengths equals the radius $r$.
  • The circumference of a circle is a little more than 6 times the length of the radius.

• Nuclear Size and Density

  • Nuclear size is defined by nuclear radius; nuclear density can be calculated from nuclear size.
  • Nuclear size is defined by nuclear radius, also called rms charge radius.
  • The problem of defining a radius for the atomic nucleus is similar to the problem of atomic radius, in that neither atoms nor their nuclei have definite boundaries.
  • Rutherford was able to put an upper limit on the radius of the gold nucleus of 34 femtometers (fm).
  • This gives a charge radius for the gold nucleus ($A=197$) of about 7.5 fm.

• Ionic Radius

  • Ionic radius (rion) is the radius of an ion, regardless of whether it is an anion or a cation.
  • When an atom loses an electron to form a cation, the lost electron no longer contributes to shielding the other electrons from the charge of the nucleus; consequently, the other electrons are more strongly attracted to the nucleus, and the radius of the atom gets smaller.
  • The ionic radius is not a fixed property of a given ion; rather, it varies with coordination number, spin state, and other parameters.
  • Nevertheless, ionic radius values are sufficiently transferable to allow periodic trends to be recognized.
  • Identify the general trends of the ionic radius size for the periodic table.

• Compositional Balance

  • In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter.
  • By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.
  • The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it.
  • The inner radius of a ring, tube or other hollow object is the radius of its cavity.
  • The name "radial" or "radius" comes from Latin radius, meaning "ray" but also the spoke of a circular chariot wheel.

• Overview of Non-Uniform Circular Motion

  • 1: The radius of circle is constant (like in the motion along a circular rail or motor track).
  • A particle moving at higher speed will need a greater radial force to change direction and vice-versa when the radius of the circular path is constant.
  • The circular motion adjusts its radius in response to changes in speed.
  • This means that the radius of the circular path is variable, unlike the case of uniform circular motion.
  • In any eventuality, the equation of centripetal acceleration in terms of "speed" and "radius" must be satisfied.

• Problems

  • If you assume that the flow rate is constant and the flow is initially vertical, calculate the height of the water downstream of the jump as a function of the radius of the jump and the flow rate.
  • If the bathtub is large compared to the radius of the jump and the walls are vertical, how does the radius of the jump change with time?

• Angular Position, Theta

  • We define the rotation angle$\Delta \theta$ to be the ratio of the arc length to the radius of curvature:
  • The arc length Δs is the distance traveled along a circular path. r is the radius of curvature of the circular path.
  • We know that for one complete revolution, the arc length is the circumference of a circle of radius r.
  • The radius of a circle is rotated through an angle Δ.

• Applications to Economics and Biology

  • Since we can assume that there is a cylindrical symmetry in the blood vessel, we first consider the volume of blood passing through a ring with inner radius $r$ and outer radius $r+dr$ per unit time ($dF$):
  • where $v(r)$ is the speed of blood at radius $r$.
  • where $R$ is the radius of the blood vessel.