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DYNAMICS - CASE STUDY

    Introduction


Problem Animation
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At Studebaker's new Super Auto Showcase, an inexperienced salesperson drives a pickup truck toward the edge of the giant carousel while the carousel is still rotating. Look out!

What is known:

  • The carousel has a 15 meter radius and is spinning with a constant angular velocity, ωo, of 0.05 rad/s.
  • The center of mass of the truck is initially 4 meters from the center of the carousel.
  • The truck travels in a radial path across the disk with a velocity of vr(t) = 0.0889t m/s.


Problem Diagram

   
  Question

 

What are the velocity and acceleration of the truck when its center of mass is 14 meters from the center of the carousel?

   
  Approach

 
  • The motion of the truck can easily be described using polar (radial and transverse) coordinates.
  • The theory section will develop equations for velocity and acceleration in polar coordinates that make it easier to determine the velocity and acceleration of the truck