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2D Motion: Changes in Direction and Acceleration

Explore the concept of acceleration in 2D motion, where changes in velocity can occur both parallel and perpendicular to the motion. Discover how acceleration affects speed and direction through graphical examples and understand the components of acceleration in different scenarios.

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2D Motion: Changes in Direction and Acceleration

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  1. Change in direction; perpendicular to v Change in speed; parallel to v Graphically: Imagine an object moving along the following trajectory at constant speed. Take the positions at times t and Δt and find the average acceleration between them: The big new thing in 2D: changes in direction An object can move at constant speed and still have a ≠0! This didn’t happen in 1D!!

  2. (a) Acceleration in the direction of the velocity changes the speed. • (b) Acceleration perpendicular to the velocity does not change the speed but shifts the direction of the motion. In 2 (or 3) dimensions, acceleration can occur both parallel to velocity or perpendicular to it

  3. Example: Shown below are the trajectory of a moving object and the snapshots taken every second. Which of the following is true about the components of the acceleration? 4s y 3s 2s x 1s A) ax = 0, ay > 0 B) ax > 0, ay > 0 C) ax < 0, ay = 0 Note: Both the speed and the direction of velocity are changing! 4s 3s 2s v(3) 1s v(2) v(1) v(1)

  4. Circular motion T - period f =1/T - frequency -angular frequency, or angular speed r If then - angular acceleration

  5. Acceleration of uniform circular motion (centripetal or radial acceleration) r

  6. Acceleration of a Point in Circular motion Tangential acceleration Net Acceleration Radial or centripetal acceleration • The radial acceleration is given by arad=v²/r=r² • If  is constant there is no tangential component • In general, atan=r • Only the tangential acceleration changes the speed of the point

  7. Example: Period of a satellite motion g R

  8. Example: Two balls attached to a string as shown at 0.20 m and 0.40 m from the center move in circles at a uniform frequency of 20 rpm. a. What are their linear speeds? b. What are their periods? Example:The ferris wheel in the figure rotates counterclockwise at a uniform rate. What is the direction of the average acceleration of a gondola as it goes from the top to the bottom of its trajectory? A. Down B. C. The acceleration is 0 because the motion is uniform.

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