PHYS16 – Lecture 24

Ch. 10 & 11 Rotation

Announcements

• Final Exam and Midterm Exam test times– No consensus on midterm – didn’t realize during

room picking for next year– No consensus on Final

• As of right now exams will be given as before, during lab and during our final exam time.

• Problem 9 on homework, Friction =10.5 kN

• Angular Motion– Angular displacement, velocity, & acceleration– Constant acceleration problems

• Angular Inertia• Angular Energy– Rotational Kinetic Energy

• Angular Force & Torque• Angular Momentum & Collisions

Ch. 10 & 11 Rotation

Rotation pre-question

• Two ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turning disk at a fair. The ponies both simultaneously start walking toward the center of the disk. As they walk what happens to the angular speed of the disk? (Ignore friction.)A) Angular speed increasesB) Angular speed decreasesC) Angular speed stays constant

Angular Momentum & Collisions

Angular Momentum

• Angular momentum (L) – momentum of a rotating object

• Angular momentum is conserved if there are no external torques

IrpL

prL

)sin(

0L

Discussion Question: Rotating person

• When I rotate in a chair with two weights extended and then bring the weights in, what happens to my angular speed?

ΔL=0 and L=IωHolding arms out increases I.If L stays the same, and I increases thenω decreases.

What about Kinetic Energy?

Discussion Question: Rotating person

• What if I am at rest in a chair and I spin up a bicycle wheel, will I start to rotate? Which direction?

ΔL=0 , so as long as there is nooutside torques then yes, I willrotate. Direction will be oppositeto wheel.

http://www.phys.unt.edu/~klittler/demo_room/mech_demos/Rotating%20Stool%20&%20Bicycle%20Wheel.jpg

Problem

• A 50 g ball of clay is thrown at 10 m/s tangent to the edge of a 2 kg 30-cm-diameter disk that can turn. The clay hits the edge of disk and sticks. If disk initially at rest, what is angular speed after? (Ignore friction.)

rad/s 32

1

0

22

,,,

f

fdiskfclayiclay

fdiskfclayiclay

rmrmrvm

LLL

L

r

vi

Rotation pre-question

• You are unwinding a large spool of cable. As you pull on the cable with a constant tension and at a constant radius, what happens to α and ω? A) Both increase as the spool unwindsB) Both decrease as the spool unwindsC) α increases and ω decreasesD) α decreases and ω increasesE) α stays constant and ω increases

Rotation pre-question

• An ice skater spins with his arms extended and then pulls his arms in and spins faster. Which statement is correct?A) His kinetic energy of rotation does not change

because energy is conservedB) His kinetic energy of rotation increases because

angular velocity increasesC) His kinetic energy of rotation decreases because

rotational inertia is decreasing

Rotation pre-question

• Two ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turning disk at a fair. The ponies both simultaneously start walking toward the center of the disk. As they walk what happens to the angular speed of the disk? (Ignore friction.)A) Angular speed increasesB) Angular speed decreasesC) Angular speed stays constant

Application: Gears

Gears: What are they good for?

1) Transfer rotational motion2) Adjust the direction of motion

3) Change the torque….4) Change the angular velocity…

Simple Machine = Gears and Belts

• Gears are machines that transfer rotational motion

• Gear/belt system linear velocity is equal

ratiogear r

r

1

2

2

1

2211

21

rr

vv

Trade radius for rot. speed

Gear Ratio

• Gears with Teeth

• Belts or Smooth disks

1

2

2

1

r

rratiogear

f

f

2

1

2

1

teethof#

teethof#

r

rratiogear

How can we use this property?

• Angular speed decreases with increasing radius

• Torque (rotational equivalent of force) changes with radius

• Power depends on τ and ω, stays constant

)sin( rF

tdt

dWP

r

v

Trade torque for ang. speed

How can we use this property?

• Let’s assume we apply a force to rotate one gear = driver gear, and it rotates another gear = driven gear

driver

driven

driven

driver

driver

driven

r

r ratiogear

Example Question: Bicycle

• A bike is set such that it has 44 teeth on the front pedalling gear and 11 teeth on the rear gear attached to the wheel– What is the use of this setting?

• Then in a “Granny” setting it has 15 teeth on the front gear and 30 teeth on the rear gear– What is the use of this setting?

Gear ratio = 1/4, back wheel 4 times ang. speed of pedalsand ¼ times the torque -> Going downhill or on road!

Gear ratio = 2, back wheel 1/2 times ang. speed of pedalsand 2 times the torque -> Going uphill or on sand!

Example Question: Gears

• Which way does Gear C turn?• What is the ang. velocity of Gear C in rev/min?

Conclusions