https://www.physik.uni-leipzig.de/jvwikis/mechanics/ 2026-05-27T20:37:55+00:00 https://www.physik.uni-leipzig.de/jvwikis/mechanics/ https://www.physik.uni-leipzig.de/jvwikis/mechanics/_media/wiki/favicon.ico text/html 2024-10-26T12:19:53+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/1.1_basic_notions_of_mechanics?rev=1729937993&do=diff 1. Basic Principles * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading ---------- 1.1 Basic notions of mechanics Definition 1.1 System A mechanical system is comprised of particles labeled by an index $i\!\in\!\mathbb{I}$, that have masses $m_i$, reside at the positions $\mathbf x_i$, and move with velocities $\mathbf v_i$$\mathbf x_1$$\mathbf x_2$$\mathbb{R}^3$$N=2$$D=3$$N$$D$$D\,N$$\mathbf q$$\math… text/html 2022-04-01T19:28:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/1.2_dimensional_analysis?rev=1648834116&do=diff 1. Basic Principles * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading ---------- 1.2 Dimensional analysis Mathematics does not know units. Experimental physicists hate large sets of parameters because the sampling of high-dimensional parameter space is tiresome. A remedy to both issues is offered by the Buckingham-Pi-Theorem. We state it here in a form accessible with our present level of mathematica… text/html 2022-04-01T19:28:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/1.3_order-of-magnitude_guesses?rev=1648834122&do=diff 1. Basic Principles * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading ---------- 1.3 Order-of-magnitude guesses Many physical quantities take a value close to one when they are expressed in their “natural” dimensionless units. When the choice is unique, then clearly it is also natural. Otherwise, the appropriate choice is a matter of experience. We will come back to this when we employ non-dimensiona… text/html 2022-04-01T19:28:49+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/1.4_problems?rev=1648834129&do=diff 1. Basic Principles * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading ---------- 1.4 Problems Problem 1.6: \label{quest:DimAnalysis-10} Dimensional Analysis of Flight Trajectories * How does the initial velocity $v_0$ impact the distance $W$ of a thrown object (stone, ball, or shot) or a jump?$v_0$$F$$M$$L$$m=200\,\text{g}$$L$$g \simeq 10\,\text{m/s}^2$$L$$g$$H$$G\,M/R^2$$G$$M$$R$$g_M$$g=10\,\te… text/html 2022-04-01T19:28:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/1.5_further_reading?rev=1648834137&do=diff 1. Basic Principles * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading ---------- 1.5 Further reading The first chapter of Grossmann (2012) provides a clear and concise introduction to basic calculus with an emphasis on applications to physics problems. The introductory chapters of text/html 2021-10-07T06:01:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap1/basics?rev=1633579270&do=diff 1. Basic principles -Ilhador-/wikimedia, Public domain At the end of this chapter we will be able to estimate the speed of a Tsunami wave. * 1.1 Basic notions of mechanics * 1.2 Dimensional analysis * 1.3 Order-of-magnitude guesses * 1.4 Problems * 1.5 Further reading The Chapter is also available as [PDF file].