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Angular Acceleration

Angular Acceleration. .  i. .  f. . . D. w. . The direction of a is NOT given by the Right Hand Rule (RHR). a. º. D. t. Operational definition of . . A spinning wheel gradually slows. Find the vector . .  o =4p rad/s. x. a=p rad/s/s. . . a. .

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Angular Acceleration

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  1. Angular Acceleration

  2. i  f   D w  The direction of a is NOT given by the Right Hand Rule (RHR). a º D t Operational definition of   • A spinning wheel gradually slows. Find the vector . 

  3. o=4p rad/s x a=p rad/s/s   a  More of the same: • You throw a ball straight up into the air with initial velocity of 20 m/s. How many seconds before it stops at the top? How long before the wheel stops?

  4.  Serious Injury Wheel of Death • The w vector does not get longer or shorter - just changes direction What direction for a? What does this remind you of?

  5. See the magic! vf = vo + a t wf = wo + at x = 1/2 (vo + vf) t q = 1/2 (wo + wf) t x = vo t+ 1/2 a t2 q = wo t+ 1/2 at2 vf2 = vo2+ 2ax wf2 = wo2+ 2aq

  6. Sample Problem: • The drill bit of a variable-speed electric drill has a constant angular acceleration of 2.50 rad/s2. The initial angular speed of the bit is 5.00 rad/sec. After 4.00 seconds: A) what is the bit’s angular speed, and B) what angle has the bit turned through?

  7. See the magic! vf = vo + a t wf = wo + at x = 1/2 (vo + vf) t q = 1/2 (wo + wf) t x = vo t+ 1/2 a t2 q = wo t+ 1/2 at2 vf2 = vo2+ 2ax wf2 = wo2+ 2aq

  8. One more time: • A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 18.5 rad/s to 14.1 rad/s, during which the angular displacement is 85.1 rad. Determine the time it takes for the ball to slow down and its angular acceleration.

  9. T T for tangential Where is ac greatest on a merry-go-round? ac = v2/R

  10. The radian is defined: Dq= s/R Dt Dt Dq R The further out - the faster s=RDq s vT=Rw

  11. Merry-go-round revisited: ac = v2/R T but, vT = R ac = (R)2/R = R2 2/R = 2R

  12. What is Jeff’s velocity relative to the ground? Jeff v = 5 m/s v = 30 m/s Greg

  13. Now what is Jeff’s velocity relative to the ground? Jeff v = 5 m/s v = 5 m/s Greg

  14. vT=Rw w vT=Rw Car on a lift: vcar= 0

  15. Now lower the car slowly: vcar= 0 vT=Rw vT=Rw

  16. vcar= 0 vT=Rw vT=Rw Now lower the car slowly:

  17. vcar= 0 vT=Rw vT=Rw Now lower the car slowly:

  18. vcar= 0 vT=Rw vT=Rw What do you hear when the wheels touch the road?

  19. vT=Rw vT=Rw Move the lift so it makes no sound when it lands: v=?

  20. Remember: Jeff v = 5 m/s v = 5 m/s Greg

  21. vT=Rw vT=Rw Move the lift so it makes no sound when it lands: Rolling condition: vCar = Rwheel wwheel v=? Rw

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