Sections 14.2, 15.1, 15.7 PRINCIPLES OF MECHANICS A force F(x,y,z) acts on a particle of mass m and moves it from point P(x,y,z) at time t, to point P2(x2,Y2,2) at time t2 along curve C. The velocity of the particle is v, at P1 and v2 at P2. 1 ? 14 ARC LENGTH S TIME t P(x, y, z ) 12 /10- up P, (x, y,2) TIME t, ARA LENGTH 5, 12~ 15 CURVE C 5 TIME +2 ARE LENGTH 5 2 5 y X
_Sections 14.2, 15.1, 15.7 PRINCIPLE OF IMPULSE AND MOMENTUM m? + [ F dt = mv2 +1 PRINCIPLE OF IMPULSE OF TORQUE AND ANGULAR MOMENTUM $2 ¡¡ ×m? + [rxF dt = ?2 X m?2 *1 PRINCIPLE OF WORK AND ENERGY 1 2 1 2 mv + 2 1 J F . dr = = mv 2 2 P > P2 : C
Sections 14.2, 15.1, 15.7 DEFINITIONS mv is the linear momentum of the particle 1 -mv2 is the kinetic energy of the particle 2 Txmv is the angular momentum of the particle 12 F dt is the impulse of F +1 12 [FxF dt is the impulse of the torque of F +1 F . dr is the work done by F > P2 : C PRINCIPLES Principle of Impulse and Momentum Impulse of a force on a particle changes the particle's momentum. Principle of Impulse of Torque and Angular Momentum Impulse of a torque on a particle changes the particle's angular momentum. Work done by a force on a particle changes the particle's kinetic energy. Principle of Work and Energy