Introductory Rotational Dynamics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Angular Momentum ◽  
Angular Displacement ◽  
Rigid Bodies ◽  
Rotational Dynamics ◽  
Circular Motion ◽  
Uniform Rotation ◽  
Chemical Systems ◽  
Inertial Frames ◽  
Rotating Frames ◽  
Special Case

This chapter discusses the importance of circular motion and rotations, whose applications to chemical systems are plentiful. Circular motion is the book’s first example of a special case of motion using the laws developed in previous chapters. The chapter begins with the basic definitions of circular motion; as uniform rotation around a principle axis is much easier to consider, it is the focus of this chapter and is used to develop some key ideas. The chapter discusses angular displacement, angular velocity, angular momentum, torque, rigid bodies, orbital and spin momenta, inertia tensors and non-inertial frames and explores fictitious forces as well as transformations in rotating frames.

scholarly journals Generating mechanisms for spiral waves

1970 ◽  
Vol 38 ◽  
pp. 331-333
Author(s):  
D. Lynden-Bell
Keyword(s):  
Angular Momentum ◽  
Minimum Energy ◽  
Spiral Wave ◽  
Natural Oscillation ◽  
Angular Frequency ◽  
Random Motion ◽  
Circular Motion ◽  
Single Star ◽  
Energy Store ◽  
Image Position

To maintain the spiral structure over long periods in spite of the chaotic disturbances so often seen in galaxies it is probably necessary to have a large energy store which is gradually tapped to generate and maintain the spiral wave. Now in a sense stable axially symmetrical model galaxies are configurations of minimum energy for a given angular momentum structure. By a given angular momentum structure I mean that the function μ(h)dh giving the total mass with specific angular momentum between h and h + dh is given and in making the minimum energy statement I have assumed that there is sufficient ‘random’ motion to satisfy Toomre's local stability criterion. To tap a store of energy one must either tap the energy of the whole rotational structure by finding disturbances that may change μ(h), or one may tap the smaller energy store of the ‘random’ motions. Clearly the larger energy store is the more attractive. Now μ(h) is conserved for any axially symmetrical time dependent motions so the only disturbances that can change μ(h) are non-axially symmetrical. If one considers a single star moving in nearly circular motion and interacting with a weak disturbance in the gravitational potential which may be Fourier analysed into components of the form S(R) exp[i(mΦ+ωt)] then one finds that the energy and angular momentum of the star oscillate but do not change in the mean. This statement is untrue when the force due to the wave does not average to zero or when it resonates with the natural oscillation of the star about the circular motion. The angular frequency of the force seen by the star is ω + mΩ, where Ω(R) is the rotational angular velocity of the galaxy, so the exceptions occur at the resonances Here κ(R) = (4B(B-A))1/2, the epicyclic angular frequency, and A(R) and B(R) are Oort's constants. At the radius where ω + mΩ(R) = 0 the pattern of the disturbance moves around at the same velocity as the circular motion of the stars epicentre. The other resonances that were discovered by B. Lindblad lie one within and one outside that circle.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

Effect of the Critical Angular Momentum on Incomplete Fusion Dynamics

2015 ◽  
Vol 3 (1) ◽  
pp. 13-17
Author(s):  
D. Singh ◽  
◽  
S. Bharti Linda ◽  
Pankaj Kumar Giri ◽  
H. Kumar ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Incomplete Fusion ◽  
Critical Angular Momentum

Advanced Mode Unity Using Loop Antennas Proximate to Reflector for Orbital Angular Momentum Communication

2018 ◽  
Author(s):  
Ryohei Yamagishi ◽  
Hiroto Otsuka ◽  
Ryo Ishikawa ◽  
Akira Saitou ◽  
Hiroshi Suzuki ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Loop Antennas
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