1 / 7

7. System of particles

7. System of particles. Center of mass. 1 – Definition . If O is any point in the plane, the center of mass G of n particles A i , coefficiented by m i , is defined by:. A 2 (m 2 ). A 1 (m 1 ). A 3 (m 3 ). G. O. 2 – Characteristic property. . A n (m n ).

sharis
Download Presentation

7. System of particles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7. System of particles • Center of mass 1 – Definition. If O is any point in the plane, the center of mass G of n particles Ai, coefficiented by mi, is defined by: A2 (m2) . A1 (m1) . A3(m3) . G . O . 2 – Characteristic property . An(mn) B. Rossetto

  2. 7. System of particles • Momentum A2(m2) . 1 – Definition. Momentum of the sytem referred to any origin O: A1(m1) . A3(m3) . G . O . 2 – Property: from the definition of CM: . An(mn) Particularly, the momentum of the system referred to G is null: B. Rossetto

  3. 7. System of particles • Fundamental theorem (Newton 2nd law) 1 – Action-reaction « principle ». Consider a system of n particles. From the inertia principle applied to the system, the sum of internal forces is null. .G(M) System 2 – Theorem of the center of mass: or The CM moves as if it were a particle of mass equal to the total mass and if all the external forces were applied to it. B. Rossetto

  4. 7. System of particles • Angular momentum theorems (1) Theorem 1 B. Rossetto

  5. 7. System of particles • Angular momentum theorems (2) Lemma Theorem 2. From the precedent results: The CM moves as if the only external torques were applied to it. B. Rossetto

  6. 7. System of particles • Theorems rCM : location of the center of mass referred to an inertial frame /Oxyz vCM : velocity of the center of mass /Oxyz P , L : total momentum, angular momentum of the system /Oxyz P/CM , L/CM : momentum, angular momentum of the system referred to the center of mass Fext,text : external force, torque, M: total mass of the system B. Rossetto

  7. 7. System of particles • Relative motion and reduced mass The relative motion of two particles subject only to their mutual interaction is equivalent to the motion, relative to an inertial observer, of a particle of mass equal to to the reduced mass under a force equal to their interaction. Proof: Example: sun and eath isolated or earth and moon (isolated…) B. Rossetto

More Related