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?

2

6 7

4

3

1

85

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. A.

B. B.

C. It’s a tie.

D. Need more information.

A B

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. A.

B. B.

C. It’s a tie.

D. Need more information.

A B

B’s greater velocity reverses more often.

• Direction changes with position– Toward the center of the turn

Centripetal Acceleration

• 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 t?

r

r0

rt

Circular Velocity and Acceleration

v r always

r0

rt

vt

v0

Circular Velocity and Acceleration

Similar triangles

v0

vt

v

r

r0

rt

vv

rr=

Circular Velocity and Acceleration

vv

rr=

vt

= art

= vvt

rt

=1v

1r

=av

vr

a =v2

r

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 information.

A travels a greater distance in each cycle.

AB

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 information.

A and B complete a rotation in exactly the same time.

AB

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 information.

A has a greater velocity change in the same time.

AB

Another View

r

circumference = 2rspeed v = 2r/T

v

circumference = 2vacceleration a = 2v/T

va

a =

2 2 rT

T = 42rT2

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 EarthEarth rotates to the East

Source: Strahler and Strahler, Introducing Physical Geography, 2005.

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 EarthWhat happens in the Southern Hemisphere?

Source: Strahler and Strahler, Introducing Physical Geography, 2005.

Trajectories deflect right in S hemisphere

Southern Hemisphere CyclonesCyclone 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.