Transcript L10_rotation

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.