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
Ch. 10 & 11 Rotation
• Angular Motion
– Angular displacement, velocity, & acceleration
– Constant acceleration problems
• Angular Inertia
• Angular Energy
– Rotational Kinetic Energy
• Angular Force & Torque
• Angular Momentum & Collisions
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 increases
B) Angular speed decreases
C) Angular speed stays constant
Angular Momentum & Collisions
Angular Momentum
• Angular momentum (L) – momentum of a
rotating object
  
Lrp
L  rp sin(  )  I
• Angular momentum is conserved if there are
no external torques

L  0
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=Iω
Holding arms out increases I.
If L stays the same,
and I increases then
ω 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 no
outside torques then yes, I will
rotate. Direction will be opposite
to 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.)
vi
r

L  0
Lclay,i  Lclay, f  Ldisk, f
1
mclay rvi  mclay r 2 f  mdisk r 2 f
2
 f  3 rad/s
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)
B)
C)
D)
E)
Both increase as the spool unwinds
Both decrease as the spool unwinds
α increases and ω decreases
α decreases and ω increases
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 conserved
B) His kinetic energy of rotation increases because
angular velocity increases
C) 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 increases
B) Angular speed decreases
C) Angular speed stays constant
Application: Gears
Gears: What are they good for?
1) Transfer rotational motion
2) 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
v1  v2
1r1  2 r2
r1 2

 gear ratio
r2 1
Trade radius for rot. speed
Gear Ratio
• Gears with Teeth
r1 # of teeth 1
gear ratio  
r2 # of teeth 2
• Belts or Smooth disks
r1 f 2
gear ratio  
r2
f1
How can we use this property?
• Angular speed decreases with increasing
v
radius

r
• Torque (rotational equivalent of force)
changes with radius
  rF sin(  )
• Power depends on τ and ω, stays constant
dW 
P

 
dt
t
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
rdriven driver  driven
gear ratio 


rdriver driven  driver
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?
Gear ratio = 1/4, back wheel 4 times ang. speed of pedals
and ¼ times the torque -> Going downhill or on road!
• 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 = 2, back wheel 1/2 times ang. speed of pedals
and 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