XXXIX. The problem of uniform rotation treated on the principle of relativity

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.

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Galilean Relativity

10.1093/oso/9780199658633.003.0003 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Inertial Frame ◽

Vertical Component ◽

Horizontal Component ◽

The Other ◽

One Dimension ◽

Everyday Experience ◽

Low Speed ◽

Principle Of Relativity ◽

Galilean Relativity ◽

Laws Of Motion

Galilean relativity is a useful description of nature at low speed. Galileo found that the vertical component of a projectile’s velocity evolves independently of its horizontal component. In a frame that moves horizontally along with the projectile, for example, the projectile appears to go straight up and down exactly as if it had been launched vertically. The laws of motion in one dimension are independent of any motion in the other dimensions. This leads to the idea that the laws of motion (and all other laws of physics) are equally valid in any inertial frame: the principle of relativity. This principle implies that no inertial frame can be considered “really stationary” or “really moving.” There is no absolute standard of velocity (contrast this with acceleration where Newton’s first law provides an absolute standard). We discuss some apparent counterexamples in everyday experience, and show how everyday experience can be misleading.

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Improvements of the Equipment for Acquiring the Uniform Rotation by Self-Maintained Vibration

Zisin (Journal of the Seismological Society of Japan 2nd ser ) ◽

10.4294/zisin1948.4.1_23 ◽

1951 ◽

Vol 4 (1) ◽

pp. 23-35

Author(s):

K. TAJIME

Keyword(s):

Uniform Rotation

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Research of the Workpiece-Stage Control System Based on the ACR9000 in the Composite Coating Equipment of MEVVAII and FAD

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.668.410 ◽

2013 ◽

Vol 668 ◽

pp. 410-414

Author(s):

Rui Xia Zhang ◽

Bin Liao ◽

Zhi Guo Liu ◽

Xian Ying Wu

Keyword(s):

Control System ◽

Servo Control ◽

Uniform Rotation ◽

Coating Films ◽

Servo Control System ◽

Motion Modes ◽

Speed Rotation ◽

Micro Tools ◽

First Time ◽

Better Than

In order to realize the extensive application of technologies of MEVVAII and FAD, the composite equipment has been developed for surface modification and coating films. In this paper, for the first time, the servo control system based on ACR9000 has been used to control workpiece-stage of the composite equipment. Eight target disks are installed on workpiece-stage. Each of target disks can be mounted about 1300 PCB micro tools. So, the equipment can satisfy the requirement for mass production. Experimental results show that the coating unevenness is less than ±14%, better than those of traditional equipments which is less than ±29%. The main purpose of the paper is to introduce the design of workpiece-stage and its three motion modes of rotary positioning, uniform rotation and variable speed rotation, and coating effects corresponding to three motion modes have been verified by experiments.

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