[{"data":1,"prerenderedAt":52},["ShallowReactive",2],{"topic-en-theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics":3},{"topic":4,"trail":13,"children":23,"tasks":48,"alternates":49},{"id":5,"name":6,"locale":7,"path":8,"seo_title":6,"seo_description":9,"seo_text":10,"content_html":11,"content_chunks":12},294,"General Theorems of Particle Dynamics","en","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics","Momentum, angular momentum, work, kinetic and potential energy, and conservation laws for a particle.","This section brings together momentum and energy methods for particle dynamics, including impulse, angular momentum, work, energy, and conservation laws.","\u003Cp>\u003Cstrong>General theorems of particle dynamics\u003C\u002Fstrong> provide alternatives to direct integration of the differential equations of motion. They relate changes in motion quantities to force impulse, force moments, and work.\u003C\u002Fp>\u003Ch2>Momentum methods\u003C\u002Fh2>\u003Cp>Linear momentum characterizes translational motion of a particle. The impulse-momentum theorem relates the change in momentum over a time interval to the impulse of the resultant force.\u003C\u002Fp>\u003Ch2>Angular momentum\u003C\u002Fh2>\u003Cp>Motion relative to a point or axis can be characterized by angular momentum. Its rate of change is determined by the moment of the acting forces about the same reference point or axis.\u003C\u002Fp>\u003Ch2>Work and energy\u003C\u002Fh2>\u003Cp>The work-energy theorem relates changes in speed to the work of forces and can often eliminate time from the analysis. For conservative forces, potential energy is introduced, leading under appropriate conditions to conservation of mechanical energy.\u003C\u002Fp>",[],[14,18,22],{"id":15,"name":16,"path":17},81,"Theoretical Mechanics","theoretical-mechanics",{"id":19,"name":20,"path":21},138,"Dynamics","theoretical-mechanics\u002Fdynamics",{"id":5,"name":6,"path":8},[24,28,32,36,40,44],{"id":25,"name":26,"path":27},252,"Linear Momentum of a Particle. Impulse of a Force","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Flinear-momentum-of-a-particle-impulse-of-a-force",{"id":29,"name":30,"path":31},253,"Angular Momentum of a Particle","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Fangular-momentum-of-a-particle",{"id":33,"name":34,"path":35},254,"Work of a Force. Power","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Fwork-of-a-force-power",{"id":37,"name":38,"path":39},255,"Kinetic Energy of a Particle. Work-Energy Theorem","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Fkinetic-energy-of-a-particle-work-energy-theorem",{"id":41,"name":42,"path":43},256,"Potential Force Field. Potential Energy","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Fpotential-force-field-potential-energy",{"id":45,"name":46,"path":47},257,"Conservation of Mechanical Energy","theoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics\u002Fconservation-of-mechanical-energy",[],{"en":50,"uk":51},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Ftheoretical-mechanics\u002Fdynamics\u002Fgeneral-theorems-of-particle-dynamics","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fteoretychna-mekhanika\u002Fdynamika\u002Fzahalni-teoremy-dynamiky-materialnoi-tochky",1787712537092]