PHYS16 – Lecture 24
Simple Machines II and Static Equilibrium
November 3, 2010
Review of last time…
Practice Question 1
• In a spin, why do ice skaters decrease their
ang. velocity when they hold their arms out?
A)
B)
C)
D)
E)
It decreases ang. momentum.
It decreases rot. inertia.
It increases rot. inertia.
It increases the centripetal force.
None of the above.
http://www.corbisimages.com/images/67/7760610C-6DF3-4A39-ACD6-C3CDEFF73296/PN015983.jpg
Kristi Yamaguchi
Practice Question 2
• A lawn tractor tire turns at 65.0 rpm and has a
radius of 13.0 cm. Find the linear speed of the
tractor in m/s.
A)
B)
C)
D)
0.141 m/s
0.885 m/s
88.5 m/s
186 m/s
Practice Question 3
• A ball attached to the end of a string is swung
in a vertical circle. The angular momentum of
the ball at the top of the circular path is:
A) > ang. momentum at the bottom
B) = ang. momentum at the bottom
C) < ang. momentum at the bottom
Practice Question 4
• The turbine of a jet engine has a moment of
inertia of 25 kg∙m2. If the turbine is
accelerated uniformly from rest to an angular
speed of 150 rad/s in a time of 25 s, what is
the torque?
   0  t
  (  0 ) / t
  I  I (  0 ) / t  (25)(150) / 25  150 J
This Week
• Simple Machines II – gears, belts, and levers
• Static Equilibrium
– Center of Gravity
– Newton’s Second law for torques and forces
Simple Machines II
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 2
gear ratio  
r2 # of teeth 1
• Belts or Smooth disks
r1 f 2
gear ratio  
r2
f1
Gears/Belts: What are they good for?
1) Transfer rotational motion
2) Adjust the direction of motion
3) Change the torque….
Torque and Power
• Torque (rotational equivalent of force)
changes with radius
  rF sin(  )
• Power depends on both torque and rotational
speed
dW 
P

 
dt
t
Example Question: Bicycle
• A bike is set such that it has 44 teeth on the
front gear and 11 teeth on the rear gear
– What is the use of this setting?
Going downhill or fast!
• 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?
Going uphill!
Example Question: Gears
• Which way does Gear C turn?
• What is the ang. velocity of Gear C in rev/min?
Simple Machine: Lever
• Lever is a machine that improves mechanical
advantage by using rotation
• In a lever the applied force can be reduced by
increasing the distance between force and
fulcrum
  rF sin(  )
Increasing r allows for decreasing F
Example Question: Lifting students
• If the fulcrum is placed in the middle it takes
me 1 kN of force to lift two students. Now, if I
place the fulcrum such that it is ¾ of the way
from my end, how much force do I need?
A third of the force!
Three kinds of levers: Video
• http://www.youtube.com/watch?v=PW7ztbwJ
KBk
• This movie reminds me of a high school film
strip, but is useful…
Static Equilibrium
• Forces should not cause linear acceleration


 F  ma  0
• Torques should not cause rotational
acceleration
  I  0
• Object has no rotational or linear motion
Example: Wheelbarrow
• I want to use a wheelbarrow to move 30 kg of
yard waste with a center of mass 0.2 m from
the wheel axle. If the handle is located at 1 m
from the wheel axle how much force should I
use to keep the wheelbarrow lifted?
F=(30kg)(9.8 m/s^2)(0.2 m)/(1 m) = 60 N
• What is my mechanical advantage?
MA=(30kg)(9.8 m/s^2)/(60 N) = 5
Main Points
• Gears transfer rotational motion, as the radius
of the gear increases there is more torque for
the same amount of force
• Levers use torque to lift a load, as the length
of the lever arm increases the force needed
decreases
• Static Equilibrium – both forces and torques
on an object have to sum to zero