1. Today: Finish Newton’s laws,
Linear and Angular Momentum
Newton’s Cradle: Dominique Toussaint on wikipedia
2. Exam #3 curved results
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3. FORCE…What is a force?
What can force do?
Force changes the motion of an object
gravitational force is responsible for the
elliptical orbit of the Earth / Sun.
frictional force slows down a sliding hockey
puck.
Force causes deformations in an object
electrical force causes nucleus to deform
applied force can cause a spring to stretch or
compress
4. FORCE…What is a force?
What kind of forces are there?
Fundamental: Gravity, Electromagnetic, strong, weak
Practical: Gravitational, electrical, magnetic, frictional, drag
“stretchy”, contact (hard objects)
All of these can be measured in units of “force”
Pounds or Newtons are common. 2.2 lbs. =~ 10 Newtons.
(1 kg weighs 10 Newtons on Earth)
5. A little bit about “net force”
Forces have a directionality
“Net Income” = profit after adding up all the plusses and
minuses.
“Net Force” = force after adding up all the up, down, left,
right and diagonal force vectors
Zero
10 Lbs 10 Lbs
“10 Lbs up + 10 Lbs down
= zero net force”
10 Lbs
45 deg. up
10 Lbs
45 deg. down
“10 pounds up and to the right +
10 pounds down and to the right
= 14 pounds to the right”
14 lbs right
6. Newton’s three laws of motion: review of 1st
two
1. Inertia: An object’s motion will not change unless
acted on by an external force.
2. Acceleration is proportional to force. a = F / m
7. Let’s look some more at
Newton’s first two laws, and inertia
http://www.youtube.com/watch?v=Hyw9uNF4nmE&feature=related
(excellent lecture on inertia)
(Last week we did some of our own lecture demos
(table cloth, smashing hand))
And watch this famous demo:
http://www.youtube.com/watch?v=_TKe5rBJeYc
8. Newton’s third law of motion.
“When two objects interact, the forces they exert on each other
are equal and opposite”
“For every action, there is an equal and opposite reaction.”
“For an isolated system, there is conservation of
momentum”
The Sun cannot attract the Earth without the Earth attracting the
sun…You cannot push on the bumper of a car without the
bumper of the car pushing on you.
Force Force
http://www.youtube.com/watch?
v=8deNwoczCPc&feature=related
Canon recoil
9. Linear Momentum
Also just referred to as “momentum”
Momentum is proportional to mass
Momentum is proportional to velocity (speed)
Momentum is a vector (we won’t use these)
Momentum = mass x velocity
p =m v
Like total energy, linear momentum is conserved…
cannot be created or destroyed.
Conservation of momentum is reflected
in Newton’s 1st
and 3rd
laws.
Force Force
http://canu.ucalgary.ca/map/content/force/newton3/
exploding_blocks/applet.html
10. Let’s think about conservation of momentum
Newton’s cradle demo
Momentum conserved, kinetic energy NOT conserved.
momentum = mass * velocity
kinetic energy = ½ mass * (velocity)2
“Elastic collision”
total kinetic energy
conserved
“inelastic collision”
kinetic energy lost via heat flow
Newton’s Cradle: Dominique Toussaint on wikipedia
11. Brainstorming session
Part 1 – Think of examples where linear momentum appears to NOT be conserved
Throwing clay at the wall; Car crash—inelastic collision car smashing into steel
pole; bullet into bullet proof vest; bird against the window; skier into tree; drop
something onto the ground;
Part 2 – one object was at rest other in motion, both end up at rest; objects
change shape (accounts for the inelasticity or loss of kinetic energy); always a
smaller object crashing into a much bigger object.
12. Clicker question—conservation of momentum
Consider a car at rest at a stop light. When the light
turns green, the car accelerates up to a speed of
60 mph. The momentum went from zero to
something much more than zero! Does this violate
the law of conservation of momentum???
A) Yes
B) No
13. Clicker question—conservation of momentum
Consider a car at rest at a stop light. When the light
turns green, the car accelerates up to a speed of
60 mph. The momentum went from zero to
something much more than zero! Does this violate
the law of conservation of momentum???
A) Yes
B) No
It really is a very good law of physics, so has to be “no.”
But where did the momentum come from?
14. Angular momentum is the momentum of spinning or orbiting.
For linear momentum, recall:
Momentum is proportional to mass
Momentum is proportional to velocity (speed)
momentum = mass x velocity
momentum = inertia x velocity
Angular momentum is similar:
Angular momentum is proportional to rotational inertia
Angular momentum is proportional to rotational speed
angular momentum = rotational speed x moment of inertia
Complicated!!!
15. Moment of inertia (rotational “mass”)
The further the mass from the rotation axis, the
higher the moment of inertia.
angular momentum = rotational speed x moment of inertia
16. Clicker Question—Angular Momentum
Two spinning tops have exactly the same mass and
are spinning at exactly the same angular rate
(e.g., 1000 rpm). Which of them would have more
angular momentum?
A B C
Exactly the Same
17. Clicker Question—Angular Momentum
Two spinning tops have exactly the same mass and
are spinning at exactly the same angular rate
(e.g., 1000 rpm). Which of them would have more
angular momentum?
A B C
Exactly the Same
Mass farther away from axis contributes
more to angular momentum
18. Angular momentum is conserved also!
Like total energy and linear momentum, there is “conservation of
angular momentum”…cannot be created or destroyed
If two objects are spinning in opposite directions, they have
opposite angular momentum.
“right hand rule”
Angular momentum “up”
“positive”, “spin up”
Angular momentum “down”
“negative”, “spin down”
19. Clicker question—”right hand rule”
Say I spin a top on a table. Looking at the top
from above, it is rotating counter-clockwise.
Is this top “spin up” or “spin down”?
A) spin up
B) spin down
View from above
20.
21. Clicker question—”right hand rule”
Say I spin a top on a table. Looking at the top
from above, it is rotating counter-clockwise.
Is this top “spin up” or “spin down”?
A) spin up
B) spin down
View from above
22. Does this violate law of
conservation of angular momentum?
Falling cat and angular momentum…
23. First, I want to point out how dangerous this is.
In this case, the falling cat JUST MISSED a sleeping baby!!!
Cat shaped hole
in mattress
Oblivious
sleeping baby
24. At beginning and end, cat has
Zero angular momentum.
In between it’s diffuclt to see, but
total angular momentum still zero.
We maybe can demonstrate this with
the spinning chair???
Falling cat does not violate conservation of angular momentum
25. Let’s play with some demos of
“conservation of angular momentum!”
Spinning chair / dumbells
Bicycle wheel / chair
