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Transcript
Group Work 1. Compare and contrast momentum and kinetic energy. a. Identify and describe at least one characteristic they share. b. Identify and describe at least two differences between them. Announcements Today • Exam 2, 11 AM–midnight – On Moodle – 1-hour limit – Standards 6–9 • Make-ups for standards 2–5 available – If you have done the practice problems Uniform Circular Motion Real and fictitious forces 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. • Explain the “fictitious” centrifugal and Coriolis forces in a rotating frame of reference. 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 Poll 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 Poll 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 Think 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. Think 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 Think 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 Think 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 Centripetal Acceleration • Direction changes with position – Toward the center of the turn • Magnitude = v2/r – v = tangential speed (m/s) – r = radius of turn (m) Uniform Circular Motion • Define the system r Circular Velocity and Acceleration How far does it move in time Dt? rt Dq Dr r0 Circular Velocity and Acceleration vt v r always rt Dq v0 r0 Circular Velocity and Acceleration Similar triangles Dv rt Dq Dr r0 Dv Dr v = r Dq v 0 vt Circular Velocity and Acceleration Dv =a Dt Dv Dr v = r Dv 1 Dr 1 = v Dt Dt r a v v = r v2 a= r Dr =v Dt Think 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 A B information. A travels a greater distance in each cycle. Think 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 A B information. A and B complete a rotation in exactly the same time. Poll 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 A B information. A has a greater velocity change in the same time. Another View v r circumference = 2pr speed v = 2pr/T a v circumference = 2pv acceleration a = 2pv/T 2 p 2p r 2r T 4 p a= = T T2 Rotating Frame Forces Truth or illusion? Centrifugal Force • “Fictitious” outward force felt in the accelerating frame of reference • Analogous to backward force felt in an accelerating car • Actual acceleration is always into the center of the turn! • Centrifugal force does not follow Newton’s third law: non-inertial Coriolis Force • Apparent force that deflects a path in the rotating frame of reference Coriolis Force • Trajectory is straight; observer turns beneath it Coriolis Force on Earth Earth rotates to the East Trajectories deflect right in N hemisphere Source: Strahler and Strahler, Introducing Physical Geography, 2005. Coriolis and Inrushing Air Trajectories deflect right in N hemisphere L Cyclonic Storms on Earth Hurricane Ike, September 12, 2008 NASA Earth Observatory Coriolis Force on Earth What happens in the Southern Hemisphere? Trajectories deflect right in S hemisphere Source: Strahler and Strahler, Introducing Physical Geography, 2005. Southern Hemisphere Cyclones Cyclone Monty, NW Australia, March 2, 2004 Both Hemispheres NASA Earth Observatory, September 3, 2008 Coriolis Force on Earth • The direction toilets and bathtubs drain on earth is not determined by the Coriolis force. • They are to small and they drain too quickly for the Coriolis force to matter. Reading for Next Time • Torque and angular momentum • Big ideas: – Rotational analogues of force and momentum. – Both are vectors in every sense. – Angular momentum is conserved.