Uniform Circular Motion Speed is constant direction isnt

Uniform Circular Motion Speed is constant, direction isn’t Chapter 5

What’s the point? • What makes something change direction? • What happens when an object’s speed stays constant as its direction changes?

Objectives • Relate tangential velocity, angular velocity, radius, and centripetal acceleration of an object undergoing uniform circular motion.

Question The diagram shows the positions at evenly-separated times of an object in uniform circular motion. Which shows its velocity vectors at each time? A B 2 3 4 1 5 8 6 7 C

Think Question If an object’s velocity were initially in the direction of vector A, and later in the direction of vector B, what was the direction of its acceleration? A. B. C. D. A B

Question If an object’s velocity were in the direction of vector A, what is the direction of the force that would change its velocity to B? A. B. C. D. A B

Question The diagram shows the positions at evenly-separated times of an object in uniform circular motion. Which shows its acceleration vectors at each time? A B 2 3 4 1 5 8 6 7 C

Question Two balls with the same speed contact different semicircular guides. Which reverses its direction soonest? A. Ball A. B. Ball B. C. It’s a tie. D. Need more A B information. B has smaller radius, so its velocity reverses sooner.

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

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

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

Question Points A and B are different distances from the center of a rotating disk. Which has the greater tangential speed? A. A. B. B. C. It’s a tie. D. Need more B A information. A travels a greater distance in each cycle.

Question Points A and B are different distances from the center of a rotating disk. Which reverses the soonest? A. A. B. B. C. It’s a tie. D. Need more B A information. A and B complete a rotation in exactly the same time.

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

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

Uniform Circular Motion • Define the system – r = radius – v = speed – T = period r

Velocity and Acceleration v r circumference = 2 pr speed v = 2 pr/T a v circumference = 2 pv acceleration a = 2 pv/T 2 p 2 p r 2 r T 4 p a= = T T 2

Check 4 p 2 r/T 2 • Which location has the greatest acceleration? B A • Same T at both • Greater r at A • a. A > a. B

In terms of v 4 p 2 r 2 a= = r 2 2 T T = (2 pr/T)2/r = v 2/r

Check v 2/r • Same v for both • Smaller r for B A B

Check v 2/r • Same r for both • Greater v for B A B

Circling Velocity and Acceleration Speed is constant Acceleration = a = v 2/r Direction of acceleration = direction of velocity + 90° = direction of position + 180° = opposite direction of r = into the center of the circle! dv dq vt v 0

Centripetal Force • A net force resulting in uniform circular motion – Not necessarily a single force – Toward the center – Magnitude mv 2/r