[{"data":1,"prerenderedAt":37},["ShallowReactive",2],{"topic-en-theoretical-mechanics\u002Fkinematics\u002Frelative-motion-of-a-particle-section\u002Facceleration-addition-coriolis-acceleration":3},{"topic":4,"trail":18,"children":32,"tasks":33,"alternates":34},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},224,"Acceleration Addition. Coriolis Acceleration","en","theoretical-mechanics\u002Fkinematics\u002Frelative-motion-of-a-particle-section\u002Facceleration-addition-coriolis-acceleration","Acceleration Addition and Coriolis Acceleration","Absolute, relative, transport and Coriolis acceleration of a particle in relative motion. Acceleration-addition theorem.","This topic presents the acceleration-addition theorem for a particle observed from a moving frame and explains the geometric and physical meaning of Coriolis acceleration.","\u003Cp>In relative particle motion with a rotating reference frame, absolute acceleration is not merely the sum of relative and transport accelerations. An additional term appears: \u003Cstrong>Coriolis acceleration\u003C\u002Fstrong>.\u003C\u002Fp>\u003Ch2>Acceleration-addition theorem\u003C\u002Fh2>\u003Cp>For a particle moving relative to a moving reference frame, absolute acceleration is $\\vec a_a=\\vec a_r+\\vec a_e+\\vec a_C$, where $\\vec a_r$ is relative acceleration, $\\vec a_e$ is transport acceleration, and $\\vec a_C$ is Coriolis acceleration.\u003C\u002Fp>\u003Ch2>Coriolis acceleration\u003C\u002Fh2>\u003Cp>For a particle moving relative to a reference frame rotating with angular velocity $\\vec\\omega_e$, the Coriolis acceleration is:\u003C\u002Fp>\u003Cp>$$\\vec a_C=2\\vec\\omega_e\\times\\vec v_r.$$\u003C\u002Fp>\u003Cp>Its magnitude is:\u003C\u002Fp>\u003Cp>$$a_C=2\\omega_e v_r\\sin\\theta,$$\u003C\u002Fp>\u003Cp>where $\\theta$ is the angle between $\\vec\\omega_e$ and relative velocity $\\vec v_r$. Its direction follows from the cross-product right-hand rule.\u003C\u002Fp>\u003Ch2>When Coriolis acceleration is zero\u003C\u002Fh2>\u003Cp>The term $\\vec a_C$ vanishes if the moving frame does not rotate ($\\omega_e=0$), if the particle has no relative velocity ($v_r=0$), or if $\\vec v_r$ is parallel or antiparallel to $\\vec\\omega_e$.\u003C\u002Fp>\u003Ch2>Transport acceleration\u003C\u002Fh2>\u003Cp>For a moving frame with origin $O'$, the transport acceleration of the coincident frame point contains origin acceleration, tangential rotational acceleration, and centripetal acceleration: $\\vec a_e=\\vec a_{O'}+\\vec\\varepsilon_e\\times\\vec r+\\vec\\omega_e\\times(\\vec\\omega_e\\times\\vec r)$.\u003C\u002Fp>\u003Ch2>Direction of Coriolis acceleration\u003C\u002Fh2>\u003Cp>The direction of $\\vec a_C$ follows from $2\\vec\\omega_e\\times\\vec v_r$. In planar problems, first determine the direction of $\\vec\\omega_e$ by the right-hand rule and then take its cross product with $\\vec v_r$.\u003C\u002Fp>\u003Ch2>Example\u003C\u002Fh2>\u003Cp>A disk rotates with $\\omega_e=4$ rad\u002Fs while a slider moves radially in a slot at $v_r=0.5$ m\u002Fs. Here $\\theta=90^\\circ$, so $a_C=2\\cdot4\\cdot0.5=4$ m\u002Fs². Its direction lies in the disk plane and is perpendicular to the radial relative-velocity direction.\u003C\u002Fp>\u003Ch2>Common mistakes\u003C\u002Fh2>\u003Cul>\u003Cli>omitting the factor 2 in the Coriolis formula;\u003C\u002Fli>\u003Cli>using absolute velocity instead of relative velocity $\\vec v_r$;\u003C\u002Fli>\u003Cli>adding acceleration magnitudes without accounting for direction;\u003C\u002Fli>\u003Cli>including a Coriolis term when the moving frame undergoes pure translation;\u003C\u002Fli>\u003Cli>reversing the cross-product order $\\vec\\omega_e\\times\\vec v_r$.\u003C\u002Fli>\u003C\u002Ful>",[14],{"id":15,"code":16,"type":17,"locale":7},195,"kinematics-coriolis-acceleration","formula",[19,23,27,31],{"id":20,"name":21,"path":22},81,"Theoretical Mechanics","theoretical-mechanics",{"id":24,"name":25,"path":26},137,"Kinematics","theoretical-mechanics\u002Fkinematics",{"id":28,"name":29,"path":30},287,"Relative Motion of a Particle","theoretical-mechanics\u002Fkinematics\u002Frelative-motion-of-a-particle-section",{"id":5,"name":6,"path":8},[],[],{"en":35,"uk":36},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Ftheoretical-mechanics\u002Fkinematics\u002Frelative-motion-of-a-particle-section\u002Facceleration-addition-coriolis-acceleration","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fteoretychna-mekhanika\u002Fkinematyka\u002Fskladnyi-rukh-materialnoi-tochky\u002Fdodavannia-pryskoren-pryskorennia-koriolisa",1787778342243]