1 / 28

Circular motion

Circular motion. The track cyclist leans in. The road banks. A turning airplane ‘banks’. Race drivers learn how to corner. Staying on the road on a curve is the mark of a good driver. Oops!. It all starts with the vector description of position. And my Laws!.

mandar
Download Presentation

Circular motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Circular motion

  2. The track cyclist leans in

  3. The road banks

  4. A turning airplane ‘banks’

  5. Race drivers learn how to corner

  6. Staying on the road on a curve is the mark of a good driver Oops!

  7. It all starts with the vector description of position And my Laws!

  8. An object at position r1 moves to position r2 in time Dt Motion is at constant speed; |v1| = |v2|

  9. Look at the changing velocity vectors The velocity vectors v are everywhere perpendicular to radius r.

  10. The triangle formed by r1 and r2 defines the vector Dr The triangle formed by vectors v1 and v2 is similar because the r and v vectors are mutually perpendicular. The v triangle defines the vector DV

  11. a If there’s Dv, there must be acceleration Or else its goodbye, satellite!

  12. The vector Dv points radially inwards Thus the acceleration vector a = Dv/Dt must also be radially inwards. This is called centripetal (center-seeking) acceleration.

  13. By similar triangles,

  14. Divide both sides by Dt: This is the magnitude of centripetal acceleration.

  15. Centripetal acceleration keeps you moving in a circle Without that acceleration, motion continues in a straight line.

  16. There’s a neat way to derive this using Calculus, but we’ll leave that as a challenge for you

  17. Of use is the radial unit vector:

  18. And the quantity known as angular velocity: Angular velocity is measured in radians per second.

  19. Angular velocity?

  20. There are two kinds of circular motion:

  21. Uniform Circular Motion Angular velocity (and therefore speed) are constant. The centripetal acceleration vector is directed at right anglesto the velocity vector.

  22. Non-uniform circular motion Tangential acceleration changes the angular velocity and therefore the speed of the bug. Radial acceleration only changes the direction.

  23. Non-uniform circular motion Procedure: determine |at| from the change in speed. Determine |ar|. The vector acceleration a has

  24. Problems An airplane goes into a circular dive at a speed of 550 km/hr. The pilot experiences “2.5 g’s” (pilot lingo for ‘an acceleration equal to 2.5 times earth gravity’).What must be the radius of the dive?

  25. Problems In science fiction movies, a space station rotates to provide ‘artificial gravity.’ Suppose a station that will be 300 m in radius is to rotate fast enough to provide at least ½ earth gravity for the comfort of its occupants. What should be the station’s minimum rotational speed, expressed in revolutions per minute? If you stand at the outer edge of the station and I’m at the hub, how fast do I think you are going (what is your speed in m/s)?

  26. Problems A loop-de-loop ride at an amusement park traverses a circular arc of radius 24 m. In order to keep the cars on the track when at the top of the loop, what must be theminimum speed of the ride?

  27. Magnitude of centripetal acceleration a = v2/r Since velocity is only tangential, acceleration can only be radial andtherefore acceleration only changes the direction of the velocity.

  28. Problems Going around a corner, a driver enters a curve of radius 150 m while traveling at 27 m/s.Realizing he is going too fast, he slows to 24 m/s in 4 seconds. What is the average acceleration experienced by the driver while slowing?

More Related