1. CPS Question The acceleration of an object moving at constant speed in a circular path is zero. A.True. B.False.

2. CPS Question The direction of the acceleration of an object moving at constant speed in a circular path is A.in the direction of its motion. B.opposite the direction of its motion. C.toward the center of its circular path. D.away from the center of its circular path.

3. Uniform Circular Motion Constant speed in a circular path a || = 0; a  = a What is the actual vector a?

4. Uniform Circular Motion Define the system r angular speed =  radians/s

5. Position What is position r at time t? rtrt  tt r0r0 00 Polar coordinates: r 0 = (r,  0 ) r t = (r,  t ) = (r,  0 +  )  =  t (radians) t0t0 lim  = d  =  dt

6. Circular Velocity and Acceleration How far does it move in time dt? dr d  =  dt Arc length = dr = r d  r0r0 rtrt dd 00  dt Direction =  dt +  /2 =  0 +  dt +  /2 =  r  r dt dt = r dr d = Speed = v = dr dt

7. Circular Velocity and Acceleration Velocity at time dt: dd 00  dt Polar coordinates: v dt = (  r,  dt +  /2) = (v,  dt +  /2 ) r0r0 v0v0 rdtrdt vdtvdt

8. Circular Velocity and Acceleration velocity vector rotates! v t = (v,  0 +  dt +  /2) radius = v =  r Arc length = dv = v d  v  dt dt =Acceleration = a = dv dt v d  dt = = v  = v 2 /r v r = v v0v0 vdtvdt dd dv

9. Circular Velocity and Acceleration Acceleration = a = v 2 /r v0v0 vtvt  vv Direction of acceleration = direction of velocity + 90° =  t + 90° + 90° =  t + 180° = opposite direction of r = into the center of the circle!

10. CPS Question Which of the following controls are used to accelerate a car? Enter the sum of the correct choices. 100000Steering wheel 10000Power windows 1000Brake pedal 100Gas pedal 10Defroster 1Windshield wipers

11. CPS Question Two balls with the same speed contact different semicircular guides. Which accelerates the most in the curve? A. Ball A. B. Ball B. C. It’s a tie. D. Need more information. A B B’s velocity reverses in a shorter time.

12. CPS Question A and B stand the on edge of identical carousels. B has a greater tangential speed. Which accelerates the most? A. B. C. It’s a tie. D. Need more information. AB B’s greater velocity reverses more often.

13. CPS Question Points A and B are different distances from the center of a rotating disk. Which accelerates the most? A. B. C. It’s a tie. D. Need more information. A has a greater velocity change in the same time. A B