Transcript F g - mrbernabo

Next year show how balanced torque problems
can be kept in g and cm more.
A Force causes an object to accelerate
A Torque causes an object to rotate
Torque
Force
Anytime you rotate an object you apply a torque
When you open door, it rotates. Where is
the pivot point / axis of rotation?
To open a heavy door where would you
push on the door to make it easiest?
A
B
C
The distance from the pivot point to the
location of the force is called the
LEVER ARM (distance)
A
B
C
The longer the lever arm the greater the torque
This force has no lever arm and produces no
torque or rotation
The direction of the force matters too, how well will
these two forces work for opening the door?
B
A
To Rotate an object the force must be applied perpendicular
to the lever arm (the door in this case)
B
A
A is perpendicular to the lever
TORQUE
t=Fd
Force perpendicular
to lever arm (N)
lever arm length (m)
NOT distance traveled
The greater the torque the faster an
object will rotate or turn
Where should you hold the wrench in order to
loosen a stubborn bolt?
t=Fd
Torque Force
MORE Torque
Force
A wrench is all about TORQUE
You create the most torque by holding the
wrench at the end and by exerting a large
force.
If you can’t loosen the bolt with all your
strength, what do you do?
Force
Force
Get a longer wrench!!
lever arm
Even with the same force, twice the
lever arm gives twice the TORQUE
The greater the force,the greater the torque
t=Fd
Torque
Force
Force
MORE Torque
The more perpendicular the force the
greater the torque
t=Fd
Torque
Force
only the blue
part counts
MORE Torque
Force
Any force which points through the axis
of rotation creates no torque
Force
t=Fd
Torque = 0
What is the torque generated by pushing
With a force of 5.0 N on a wrench which is
20 cm long?
Torque requirement on your tires lug nuts is 190 Nm.
If you have a wrench which is .25 m, how hard do you
have to push?
.25 m
Consider the two wrenches below, compare torques
If the applied force is the same
F
F
The lever arm distance is really still the same
F
F
Another way of looking at torque, this is easier
in some situtations.
1.) Draw a line through the force
2.) Bring a line perpendicular to the previous line
through the axis of rotation
3.) The lever arm is the distance that line
to the center of rotation
lever arm distance
4.) Torque = Total force x lever arm
1.) Draw a line through the force
2.) The lever arm is the distance that line
to the center of rotation
3.) Torque = Total force x lever arm
Lever arm distance (d)
F
1.) Draw a line through the force
2.) The lever arm is the distance that line
to the center of rotation
3.) Torque = Total force x lever arm
F
Lever arm distance (d)
A force of 100 N is exerted as below on a rope attached
to a .25 m wrench. What torque is generated?
100 N
.2 m
F
TORQUE is also a vector.
We will just
think of
torque as CW
or CCW
CCW
CW
Two 400 N children balance on a seesaw
The same force on each side, right
400 N
400 N
1m
1m
What if one child scoots in?
Forces are still equal on both sides
400 N
400 N
1m
0.5 m
BUT THE TORQUES DO NOT
400 N
400 N
1m
t = 400 Nm (CCW)
0.5 m
t = 200 Nm (CW)
Net t = 200 Nm (CCW)
To prevent an object from rotating
there can be no net TORQUE
OR
tcw = tccw
If there is no net torque then an
object does not….
Rotate
(its rotation speed does not change
is the more accurate statement)
If there is no net force then an
object does not….
Accelerate
Can a big kid and a little kid balance on a seesaw?
100 N
400 N
The bigger kid must move closer the to
fulcrum to lower his torque
400 N
?
0.25 m
100 N
1m
What is the upward force at the pivot point?
If the seesaw balances what is the weight of
the other person?
400 N
.75 m
?N
1m
If a 400 N person and a 200 N person want to
balance where should be fulcrum be placed?
400 N
200 N
d
2d
So that the lever arm is twice as much for the
200N person or 2/3 away from them
If a 500 N person and a 100 N person want to
balance on the ends of a 3 m seesaw where
should be fulcrum be placed?
500 N
100 N
d
5d
So that the lever arm is 5 x as much for the
100N person or 5/6 away from them
Correct this statement:
An object balances the
when
weight
the same
on either
weight
side
is on
of
theboth
pivotsides
pointofcreate
the pivot
equal
point
torques
A mass on a string exerts a torque on a pulley,
what is lever arm & direction of torque
DEMONSTRATION: Will the object rotate
.10 m
500 g
.25 m
500 g
Torque WS
Torque lab
Torque Feeler Demo
What causes an object to change its rotational
speed?
How do you create torque?
When does a force create NO torque?
Which force creates more torque?
NEITHER creates any TORQUE,
since they both point to the axis of rotation
Demo – balanced / unbalanced meterstick
is there a net torque?
FN = mg
Fg = mg
Is there a net force?
Is there a net torque?
FN
Fg
IfWhat
the CM
isn’t
under
a pivot gravity creates torque.
is
the
axis
of
rotation?
Is there a net force?
What
lever arm?
Does is
thethe
normal
force from the pivot create torque?
Is there a net torque?
A 6 meter long board has a weight of 800 N. If
a fulcrum is placed under it 2 m from one end,
what is the torque on it.
What torque does gravity create on a .35
kg meterstick which is supported at the
15 cm mark?
Fg
Find the center of rotation (pivot point)
Find the lever arm
Force
Fg
The object below does not fall over (rotating around its base)
Because there is NO TORQUE
What is the lever arm in these examples?
Fg
Force
If the object is tilted more, which has more torque on it due to
gravity?
Fg
Fg
Fg
Gravity exerts a torque
Will the object fall now?
Fg
A Net force causes an object to…
A Net Torque causes an object to…
When a football is kicked where is the
axis of rotation?
Through the center of mass!
Can you kick a foot ball so the it does
not rotate (end over end)?
When a force is applied through the CM.
Will it accelerate? YES
Will it rotate?
Is there torque?
What about here-Will it accelerate? YES
Will it rotate- Is there torque YES
Will it accelerate? YES
Will it rotate?
Hoverpuck Demos
A ball usually starts to rotate as is rolls down a hill
If there was no friction would a ball still spin
as it went down a hill?
Is the force of gravity causing a torque?
Fg
FN
Fg
Will the normal force cause a torque?
What else is acting on the ball
Will friction cause the ball
to rotate?
FF
FN
Fg
Free body diagrams
Rolling Down a Hill
Sliding w/o Friction
FN
FN
FF
FgX
FgX
FgY
FgY
Notice that freebody diagrams are not helpful for determining torque
only if a body will accelerate
Objects at equilibrium are perfectly stationary
We may observe 2 things
Their velocity remains 0
They do not rotate
In order for an object to be perfectly still
or at equilibrium,
2 Conditions MUST BE MET
#1 All FORCES must cancel
#2 All TORQUES must cancel
Is there a Net force on the object?
A Net Torque?
100 N
This meter stick will
only rotate...
100 N
Will this object translate or rotate?
Consider the CM the axis of rotation
100 N
100 N
Will this object accelerate or rotate?
100 N
100 N
Will this object accelerate or rotate?
100 N
100 N
100 N
Will this object accelerate or rotate?
100 N
200 N
100 N
Will this object accelerate or rotate?
100 N
50 N
Will this object accelerate or rotate?
100 N
50 N
Will this object accelerate or rotate?
100 N
50 N
Will this object translate or rotate?
100 N
150 N
50 N
A 150 N person stands in the middle of 2
scales on a board, what does each read?
150 N
75 N
Do forces cancel?
Do torques cancel?
75 N
Where should a person stand so that 1
scale reads 30 Newtons?
Forces must cancel
Torques must cancel
30 N
4d
1/4 the force of the other side
So 4 x the lever arm
150 N
d
120 N
What if a 150 N person stands 1/3 away
from one scale?
150 N
50 N
1d
2d
1/3 distance
2/3 force
Consider the person the axis of rotation
100 N
Example calculation of meterstick
practicuum lab
A meterstick has a mass of 124 g and its
center of mass is at the 56.1 cm mark. If the
fulcrum is placed at the 64 cm mark, where
should a 75 g mass be hung for it to balance?
Torque and CM WS
Meterstick Practicum
Page 365
7-15
Let’s rewrite Newton’s 1st law of motion
Linear
An object will only change velocity if a Net Force is applied.
No net Force = keeps moving at the same speed
Rotational
An object will only change its Rotational speed if a Net Torque is
applied.
No net Torque = keeps rotating at the same speed
Demo- Raw vs Hardboiled eggs
The property of mass to resist a change in motion is
INERTIA
OBJECTS HAVE BOTH:
Linear Inertia:
&
Rotational Inertia
Picture yourself running and pushing a merry go round full of
your friends verses and empty one.
The more people that are on it, the harder it is to spin!!!
(and to slow down)
The more mass on the merry go round the more it resists
changing its ROTATIONAL speed.
Rotational Inertia:
--resistance to rotational acceleration
-- depends not just on how much mass
but also the location of the mass
Demo- rotating a stick
Try waggling your leg fully extended vs. with your knees bent
Location, location, location
The further the mass is from the pivot point,
the more the ROTATIONAL INERTIA
If both have the same mass will they be the
same difficulty to spin?
The ROTATIONAL INERTIA also depends on how the
object is being spun (the axis of rotation)
Which has the higher rotational inertia
A baseball bat is harder to swing if held from the end
And harder to slowdown
A tennis racket can pivot through several axes,
which will be the EASIEST (lowest rotational inertia)
Hardest
Easiest
Consider a disc, how will it be easier to rotate?
(neglecting air resistance)
Like a record
Flat
Demo: Rolling Race
Two discs with the same mass and radius are rolled down a hill.
One is hollow and the other solid?
Which will make it to the bottom first or will it be a tie?
Pipe same mass diff diameter PVC/PVC
Pipe same diameter diff mass (same length) PVC Steel
Mass is concentrated
towards the edge away
from center of rotation.
Higher rotational inertia
Mass is distributed
uniformly
Rotational Inertia
--symbol is: I
--units are: kg m2
--depends on
Shape, Mass, Axis of rotation
(see page 157) but here are a few for examples
Hoop
spinning like a record
Hoop
spinning flat
I = mr2
I = 1/2 mr2
(see page 223 Honors text) but here are a few for examples
r
Rod
I = mr2
2
rotating through center of circle
L
Rod
I = mL2
12
rotating through CM
L
Rod
rotating about an end
I = mL2
3
What is the rotational inertia of a 1.0 kg board that is .86 m
long being swung at its end vs. its middle?
.86 m
Weight pulls it down the slope
Friction gets it rotating working
against rotational inertia
NEWTONS 2nd Law
Linear Motion
F = ma
Rotational Motion
t= I a
Rotational Motion
t= I a
For a given object (I)
t
a
the greater the torque, the faster its spin
speeds up
Rotational Motion
t= I a
For a given torque (t)
I
a
For a given torque, the bigger the
rotational inertia the slower it will spin rate
will change
2 block and tackle systems have 500 g masses
attached. Compare their rotational accelerations
more t = more a
If each is pushed with the same force on the
edge, which will accelerate faster?
Recall Momentum
Two Pieces - Inertia & Speed
Momentum = mass x velocity
p = mv
Roughly how hard it will be to get something to stop moving
But an object can also have ROTATIONAL MOMENTUM
Roughly how hard it is to get an object to stop rotating.
It also depends on TWO things
Linear Momentum
Rotational Momentum
r = mv
L = _I _w
Rotational
Inertia
rotational
velocity
If the disks are equal which has the greater
rotational momentum
Greater rotational velocity,
more momentum
The disks are rotating at the same speed,
Which has more momentum
Thick disk
Greater I =
more momentum
Thin disk
A disk and a ring of equal mass are spinning
at the same rate, which has more momentum
Greater I =
more momentum
LINEAR MOMENTUM of a system is
conserved if there are no external FORCES.
p = mv
linear momentum.
Rotational Momentum is also conserved
if there are no external______________
TORQUES
Initial = Final
L1 = L 2
I1w1 = I2w2
Consider an ice skater.
If nothing exerts a torque on her while doing a spin
(friction on ice / wind resistance / angry fan)
her rotational inertia is constant
I0w0 = Ifwf
BUT WHY does she spin
faster when she brings her arms in?
Remember rotational inertia depends on two things
How much mass
How far the mass is from the axis of rotation.
The mass of the skater doesn’t change BUT
it can be placed further or closer to the rotational axis.
(If the skater starts at the left position. How will their rotational speed change)
Start
SLOWER
FASTER
FASTER
SLOWER
Iw
0
0
w
= If
f
A tucked diver spins at 1 rotations per
second. If she extends herself quadrupling
her rotational inertia, what is her rotational
speed?
Chair Demo
Is rotational momentum conserved
if an external force is applied?
A diver can control their angle of entry by controlling their
rate of rotation
What happens to the speed of the merry go round if
if start in the middle and go to the outside?
Will you be traveling faster or slower or the same?
Linear Momentum has a direction (same as velocity)
Positive velocity
Positive momentum
Negative velocity
Negative momentum
Rotational Momentum also has a direction
(like linear momentum)
The vector direction is a little weird and we don’t need to
memorize this but it points through the axis of rotation.
Changing the axis of rotation changes the direction of its
rotational momentum
If the speed of a record 33 rpm clockwise, and it
is spun at 33 rpm Counter-clockwise. Its momentum changed
by a factor of: TWO
This is like an bouncing backwards
The rotational momentum resists changing direction.
JUST like it is hard to get a semi truck going 60 mph
N to go 60 mph S.
The greater the I
& the faster is spins-the harder it is to change
This is what makes a top stable but only while it is spinning.
Due to its center of mass it would otherwise not be stable
Even better than a top is a:
Gyroscope
bicycle wheel, flip n flyer
This is what also makes your bicycle easy to ride (while moving)
If the boy is moving forward what is the
direction of the momentum vector.
(left or right)
Demo: Bicycle wheel
The total momentum of a “system” remains constant.
(no outside torque)
Two disks at rest
The initial momentum is 0
If a person start pushing the top disc clockwise
The bottom disc will move counter clockwise
The momentum will be equal and opposite
When a helicopter starts bringing its rotors up to speed,
what happens?
If global warming causes the polar ice to melt and flow towards
the equator, what affect will this have on the earth’s rotation.
How will this affect how long a day is?
Book problems
page 165-167
17, 18, 19, 20, 27, 30, 31, 32, 35, 36
A day at the Races (part I)
(Rotational Momentum/Energy Lab)
Which shape should be the best for rolling races?
pipe
solid
sphere
solid
cylinder
I = mr2
I = 2/5 mr2
I = 1/2 mr2
Which shape should be the best for rolling races?
solid
sphere
solid
cylinder
pipe
I = 2/5 mr2
I = 1/2 mr2 hollow sphere 2
I = 2/3 mr
I=
2
mr
How does mass affect the outcome of a rolling race?
How does mass affect the outcome of “falling race”
How does radius affect the outcome of “rolling race”
How can these sportbikes lean at such impossible angles
without falling over.
THINK Center of Gravity, Centripetal Force, & Torque
Any object which is rotating possesses:
ROTATIONAL KINETIC ENERGY
Think of any real examples of how rotational kinetic energy is used
or what it does?
Turbines
generators
Flywheels
Tornado
Flywheel
Charge Time
Energy / kg
Problems
15 minutes
470 kJ
Explosion
Battery
8 hours
180 kJ
Haz Materials
Water Molecules and a Microwave
How rotating water speed up
Kinetic Energy
Linear
(translation)
Rotation
mv2
KEtrans = 2
KErot =
I w2
2
Which type of kinetic energy does a rolling ball possess?
rotational / kinetic / both
BOTH
Rolling animation