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

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 Poll Question 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 information. A B 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. B. C. It’s a tie. D. Need more information. AB B’s greater velocity reverses more often.

Think 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.

Direction changes with position –Toward the center of the turn Centripetal Acceleration Magnitude = v 2 /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  t? rr r0r0 rtrt 

Circular Velocity and Acceleration v  r always  r0r0 rtrt vtvt v0v0

Circular Velocity and Acceleration Similar triangles v0v0 vtvt  vv rr r0r0 rtrt  vv v rr r =

Circular Velocity and Acceleration vv v rr r = vv tt = a= a rr tt = v= v vv tt rr tt = 1 v 1 r = a v v r a = v2v2 r

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

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

Poll 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

Another View r circumference = 2  r speed v = 2  r/T v circumference = 2  v acceleration a = 2  v/T v a a =a = 22 2 r2 r T T = 42r42r T2T2

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 Source: Strahler and Strahler, Introducing Physical Geography, Trajectories deflect right in N hemisphere

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? Source: Strahler and Strahler, Introducing Physical Geography, Trajectories deflect right in S hemisphere

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.