Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 months ago

Please please please help me?

To study the motion of the point determining the trajectory of velocity and acceleration if the law of motion of the point is in the figure below in which a, b, w are positive constants.

Attachment image

2 Answers

Relevance
  • 3 months ago
    Favorite Answer

    The position vector r traces out an ellipse with semi-major axis a and semi-minor axis b. The parametric equation for r(t) is given. By differentiating r with respect to time you find the velocity vector. A second differentiation gives the acceleration vector.

    r(t) = ( a cos(ω t) , b sin(ω t), 0 )

    v(t) = ( - a ω sin(ω t), b ω cos(ω t), 0 )

    a(t) = ( -a ω^2 cos(ω t), - b ω^2 sin(ω t), 0)

    Note that a(t) = - ω^2 r(t)

    The trajectories in v-space and a-space are ellipses too.

  • ?
    Lv 7
    3 months ago

    What is your question? If "c(ωt)" is shorthand for "cos(ωt)" and "s(ωt)" is shorthand for "sin(ωt)," then the velocity is

    | -a·ω·s(ω·t) |

    | b·ω·c(ω·t) .|

    |........ 0 .......|

Still have questions? Get your answers by asking now.