https://www.physik.uni-leipzig.de/jvwikis/mechanics/ 2026-05-01T03:39:14+00:00 https://www.physik.uni-leipzig.de/jvwikis/mechanics/ https://www.physik.uni-leipzig.de/jvwikis/mechanics/_media/wiki/favicon.ico text/html 2022-04-01T19:59:49+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.1_motivation_and_outline?rev=1648835989&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.1 Motivation and outline: forces are vectors In mechanics we use vectors to describe forces… text/html 2024-10-26T13:02:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.2_sets?rev=1729940566&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.2 Sets In mathematics and physics we often wish to make statements about a collection of obj… text/html 2023-10-22T12:53:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.3_groups?rev=1697972000&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.3 Groups A group $G$ refers to a set of operations $t\in G$ that are changing some data or o… text/html 2024-11-09T10:12:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.4_fields?rev=1731143536&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.4 Fields Besides being of importance to characterize the action of symmetry operations like … text/html 2024-11-10T20:52:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.5_vector_spaces?rev=1731268358&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.5 Vector spaces With the notions introduced in the preceding sections we can give now the fo… text/html 2022-04-01T21:00:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.6_physics_application_balancing_forces?rev=1648839621&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.6 Physics application: balancing forces Tug of War, Nikolay Bogdanov-Belsky, 1939 wikiart… text/html 2024-12-03T23:28:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.7_the_inner_product?rev=1733264882&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.7 The inner product The position of a particle, the direction of its motion and the angle o… text/html 2022-04-01T21:13:07+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.8_cartesian_coordinates?rev=1648840387&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.8 Cartesian coordinates Theorem 2.2 entails an extremely elegant possibility to deal with v… text/html 2022-04-01T21:19:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.9_cross_products_---_torques?rev=1648840768&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.9 Cross products — torques adapted from rachaelvoorhees from arlington, va \ wikimedia C… text/html 2022-04-01T21:28:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.10_worked_example_calder_s_mobiles?rev=1648841282&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.10 Worked example: Calder's mobiles We describe here the setup of a traditional mobile wher… text/html 2022-04-01T21:30:09+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.11_problems?rev=1648841409&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.11 Problems 2.11.1 Rehearsing Concepts Problem 2.27: Tackling tackles and pulling pulleys … text/html 2022-04-01T21:55:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/2.12_further_reading?rev=1648842933&do=diff 2. Balancing Forces and Torques * 2.1 Motivation and outline: forces are vectors * 2.2 Sets * 2.3 Groups * 2.4 Fields * 2.5 Vector spaces * 2.6. Physics application: balancing forces * 2.7 The inner product * 2.8 Cartesian coordinates * 2.9 Cross products — torques * 2.10 Worked example: Calder's mobiles * 2.11 Problems * 2.12 Further reading ---------- 2.12 Further reading The second chapter of Grossmann (2012) provides a clear and concise int… text/html 2022-04-01T19:49:11+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.physik.uni-leipzig.de/jvwikis/mechanics/book/chap2/forcestorques?rev=1648835351&do=diff 2. Balancing Forces and Torques In Chapter 1 we observed that positions and velocities of particles are specified by indicating their unit, magnitude and directions. Hence, they are vectors. In the present chapter we learn how vectors are defined in mathematics, and how they are used and handled in physics. In order to provide a formal definition we introduce a number of mathematical concepts, like groups, that will be revisited in forthcoming chapters. As first important application we deal wi…