Transcript 30 Rotational Mechanics II - lindsey

Rotational Mechanics LG
April 3, 2009
Take out your 5s
Physics Expectations
• A physics textbook is available to you if you would like to
check one out.
• If you do not understand, don’t hesitate to ask. We are
available before or after school and during open lab.
• You will need a 3 ring binder or folder, notebook, pencil &
calculator for class everyday.
• Do not touch lab equipment or set-ups in the room
unless you are given permission. Do not open cabinets.
• Eating and drinking in a science classroom is prohibited.
• Cell phones and mp3 players are not to be used, taken
out, heard or even seen.
• If you miss any physics class, you are responsible to find
out what you missed and how to make it up.
• No late work will be accepted. If you have an excused
absence, it is your responsibility to make arrangements
with the teacher. If you know you will be gone, check with
the teacher before you leave.
• Missed labs or tests are to be made up within one week.
You should go to the SRC during your unstructured mods
to do this. If that is not possible, you should speak to your
grading teacher and make other arrangements before the
end of your make up period.
• If you are not working up to your potential, you may get
backscheduled. If you skip backscheduling or any physics
class, you can get a detention.
• If you were backscheduled before spring break, you are
still backscheduled.
Units
Rotational Inertia (kg·m2)
Imr
2
radius (m)
mass (kg)
Units
angular momentum (kg·m2/s)
LIω
rotational velocity
Lmvr
velocity (m/s)
mass (kg)
radius (m)
Period (T) – time to complete one cycle
Frequency (f) – number of cycles per unit time
T  1/ f
period (sec)
f 1 / T
frequency (Hz)
Example problems
1) A hamster runs on his exercise wheel, which turns around
once every 0.5 s. What is the frequency of his spin?
f=1/T
f = 1 / .5
f = 2 Hz
2) If a Sony CD player spins with a frequency of 1800 RPM,
what is the period of spin?
1800 cycles 1 min
x
 30 Hz
min
60 sec
T=1/f
T = 1 / 30
T = 0.033 s
Tangential velocity – speed perpendicular to the
center of a circle
Linear velocity
d
v
t
Tangential velocity
circumfere nce
v
time for one cycle
2r
v
T
Example problems
3) What is the radius of a tire that turns with a frequency of 11
Hz and has a tangential speed of 20.0 m/s?
T=1/f
= 1 / 11
= .09 s
v = 2πr / T
20 = 2πr / .09
r = .29 m
4) The earth rotates once every 24 hours and has a radius of 6.38 x 106 m.
If there was astronomical catastrophe that suddenly brought the earth
to a halt, what would be the tangential speed of the people at the
equator as they fly off the surface?
24 hr 60 min 60 sec
x
x
 86400 sec/day
day
1 hr
1 min
v = 2πr / T
= 2π6.38x106 / 86400
= 464 m/s
Demo
Linear velocity = distance / time
d
v
t
Rotational velocity = cycles / time
# of cycles
ω
t
cycles / sec
RPS
time (s)
linear velocity
radius
v~rω
rotational velocity
How fast does the 100 cm mark move
compared to the 50 cm mark?
• same rotational velocity
• double the linear velocity
Demo
same rotational velocity
wider end has greater linear velocity
covers more distance in same time
Which will roll down the track
without falling?
Bicycle gears change the ratio of
force applied to the petals versus
force applied to the road.
Which bicycle is in high gear?
High gear – move the pedal a little to move the bike a lot
Low gear – move the pedal a lot to move the bike a little
High Gear
Low Gear
Demos
•
•
•
•
•
Bucket ‘O Water
Twirling can
Object in Can
Penny in a Balloon
Washing Machine – Spin Cycle
Centripetal = “center-seeking” or “toward the center”
Centrifugal = “center-fleeing” or “away from the center
• Whenever an object moves in a circle, it
is accelerating because it is changing
direction. (Centripetal Acceleration)
• Acceleration is caused by a net force
acting on an object. (Centripetal Force)
• Centripetal acceleration points toward
the center, but is felt as a outward force.
This feeling is centrifugal force: there is
no actual force pushing or pulling you
away from the center.
• The “centrifugal force” is actually your
body’s inertia. Your body wants to
continue in a straight line.
Centripetal Accleration
2
Centripetal
Acceleration
(m/s2)
v
ac 
r
linear
velocity
(m/s)
radius (m)
Example Problem
5) If Mr. Lindsey’s arm is 0.60 m long, what is the
minimum speed with which he can swing the
water over his head without spilling? ( hint: ac
must be greater than 9.8 m/s2)
ac= v2/r
9.8 = v2/0.6
v2 = 5.88
v = 2.4 m/s
6) Billy’s favorite ride at the fair is the gravitron which has a
radius of 4.0 m and takes 2.0 seconds to make one full
revolution. What is Billy’s centripetal acceleration?
T= 2.0 s
r=4m
ac= ?
v = 2πr/T
v = (2π4) / 2
v = 13 m/s
ac= v2/r
ac= 132/4
ac= 42 m/s2
Centripetal Force – force that causes an
object to move in a circle
mass (kg)
Centripetal
Force
(N)
mv
Fc 
r
2
linear
velocity
(m/s)
radius (m)
Demo
Reminders
• POTW due Monday
• 39s – both sheets due next Tuesday
Extras
Animal Teeter-totter
http://www.meddybemps.com/teetertotter/index.html
CentrifugeTraining