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Mastering Kinematics in Two Dimensions | Motion Diagrams & Dynamics Guide

Explore kinematics in an x-y plane through motion diagrams, forces, velocity, and acceleration. Learn to solve 2-D kinematics problems by breaking forces into x and y components. Enhance your understanding for the final exam with detailed explanations.

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Mastering Kinematics in Two Dimensions | Motion Diagrams & Dynamics Guide

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  1. Outline Kinematics in Two Dimensions • Motion Diagrams • x-y plane • Dynamics (just add forces) Final exam: 30 questions, 3 hours

  2. Two Dimensional Motion Diagram • A two dimensional motion diagram is drawn on x-y axes • Be sure to put enough dots in to represent the motion • Recall that the velocity vectors simply connect one dot to the next dot • The acceleration vectors are found by the vector subtraction of adjacent velocities

  3. Project onto x-y plane • Our Newton’s laws of motion have worked well so far because we’ve always analysed motion in an x-y plane • Our motion diagrams have been using axes which are parallel and perpendicular to the curve at a given location • Have to project those axes onto an x-y coordinate system

  4. 2-D Motion Diagram y x What is the displacement between point 2 and 4?

  5. Project delta r How do you express in terms of x and y? y x origin

  6. r_x and r_y How do you express in terms of x and y? y x origin

  7. How About Velocity?

  8. How About Acceleration?

  9. How About Force? plus This means that all two-dimensional kinematics problems can be solved by breaking up forces into their x and y components !

  10. Common Problem ! • A force in x-direction only changes the motion along the x-direction (this means that a bouncing ball that is thrown sideways and bounces off of the floor does not have its x-direction motion changed by the normal force that made the ball bounce)

  11. A projectile

  12. Do for next class: • Read: Sections 6.3 • Suggested problems: 6.12, 6.28

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