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.

Rotational Inertia (kg·m2)

2r mI

mass (kg) radius (m)

Units

Units

ω IL

r vmL

angular momentum (kg·m2/s)

rotational velocity

velocity (m/s) mass (kg)

radius (m)

Period (T) – time to complete one cycle

Frequency (f) – number of cycles per unit time

f/1T

period (sec) frequency (Hz)

T / 1 f

Example problems1) A hamster runs on his exercise wheel, which turns around

once every 0.5 s. What is the frequency of his spin? f = 1 / Tf = 1 / .5f = 2 Hz

2) If a Sony CD player spins with a frequency of 1800 RPM, what is the period of spin?

T = 1 / fT = 1 / 30T = 0.033 s

Hz 30 sec 60

min 1x

min

cycles 1800

Tangential velocity – speed perpendicular to the center of a circle

Linear velocity

Tangential velocity

t

dv

cycle onefor time

ncecircumferev

T

rv

2

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?

sec/day 86400 min 1

sec 60 x

hr 1

min 60x

day

hr 24

v = 2πr / T

= 2π6.38x106 / 86400

= 464 m/s

Demo

Linear velocity = distance / time

t

cycles of #ω

t

dv

Rotational velocity = cycles / time

cycles / sec

RPS time (s)

linear velocity radius

rotational velocityωr ~vHow fast does the 100 cm mark move

compared to the 50 cm mark? • same rotational velocity • double the linear velocity

Demosame rotational velocity

wider end has greater linear velocity

covers more distance in same time

Which will roll down the track without falling?

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

Bicycle gears change the ratio of force applied to the petals versus force applied to the road.

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

r

va

2

c Centripetal Acceleration (m/s2)

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 = 4 m

ac= ?

ac= v2/r

ac= 132/4

ac= 42 m/s2

v = 2πr/T

v = (2π4) / 2

v = 13 m/s

Centripetal Force – force that causes an object to move in a circle

Centripetal Force (N)

linear velocity (m/s)

radius (m)r

mvF

2

c

mass (kg)

Demo

Reminders

• POTW due Monday

• 39s – both sheets due next Tuesday

Extras

Animal Teeter-totter http://www.meddybemps.com/teetertotter/index.html

CentrifugeTraining