AP PHYSICS
MONDAY 15.03.23
Week 29
STANDARDS:
P-Problem Solvers
Standards: 4D net torque changes angular momentum
of system
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Warm Up
A 2 kg ball with a radius of 0.5 m rolls
down a ramp and ends up traveling
with a velocity of 4 m/s. Use
Conservation of Energy to find How
high the ramp was
ΔU=Ktotal=1/2 mv2+1/2 Iω2
Learning Goal: SWBAT analyze the
motion of different shaped rolling
objects and determine the rotational
energy required to make them roll.
Agenda:
1. Warm Up
2. Collect HW
3. Plan AP Practice Test over spring break
4. Finish Rotational Energy Conservation Lab
Homework
Tap#17 AP Problem
Notebooks due Thursday
Test Wednesday
AP PHYSICS
TUESDAY 15.03.24
STANDARDS:
D-Disciplined Learners
Standards: 4D net torque changes angular momentum
of system
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Learning Goal: SWBAT relate angular
momentum to Torque & solve FRQ’s
Agenda:
Warm Up
Angular Momentum is a conserved
quantity just as Linear Momentum is.
For each of the following situations,
identify what should happen to the
objects angular speed in order for
angular momentum to be conserved.
A. A planet is in an elliptical orbit and
it is nearing its closest distance
from the star.
B. A child is on the merry go round
and walks away from the center
towards the outer edge.
C. A tetherball winds around its pole
after being struck by a child.
1. Warm Up
2. Review Torque Lab
3. Review Torque AP Homework Problems
Homework
#18 AP FRQ’s
AP PHYSICS
WEDNESDAY 15.03.25
E-Effective Communicators
Standards: 4D net torque changes angular momentum
of system
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Warm Up
A smooth, solid ball is released from rest
from the top of an incline. The ball rolls down
the rough incline without slipping.
a. Describe the energy transfers that occur
as the ball rolls down.
b. If the solid ball was replaced with a
smooth hollow ball of the same mass,
which ball would have a larger linear
velocity at the bottom?
Learning Goal: SWBAT review FRQ’s for
AP Torque & angular momentum exam
Agenda:
1. Warm Up
2. Review Rolling Objects Lab
3. Present homework FRQ’s to calss
Homework
Study FRQ’s for exam.
AP PHYSICS
THURSDAY 15.03.26
Warm Up
NA
STANDARDS:
P-Problem Solvers
Standards: 4D net torque changes angular momentum
of system
I –Independent Resilient Individuals
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Learning Goal: SWBAT present FRQ’s
and discuss Rotational Motion Labs
Agenda:
1. Warm Up
2. Present Problems
3. Review Rotational Motion Lab
Homework
Prepare for Quiz Tomorrow 1
FRQ
AP PHYSICS
FRIDAY 15.03.27
Warm Up
NA
STANDARDS:
P-Problem Solvers
Standards: 4D net torque changes
angular momentum of system
RST.11-12.9 Synthesize information from a range of
sources into coherent understanding of a process,
phenomenon, or concept,…
WHST.11-12.7: research to aid in problem solving
Learning Goal: SWBAT explain each step
of their FRQ with words in addition to
solving the problem.
Agenda:
1. Warm Up
2. Take FRQ quiz
Homework
Prepare for AP Test over Spring
Break
LINEAR VS ROTATIONAL EQUATIONS OF MOTION
Concept
Linear
Position
x
Displacement
Velocity
Acceleration
Equation of Motion #1
Rotational
θ,
Dx = x - x0
Dx
v=
Dt
a=
Dv
Dt
v = v0 + at
x*
q=
r
Dq = q - q0
w=
v
Dq
w=
r
Dt ,
a=
Dw
Dt
a
,a =
r
w = w0 + at
Equation of Motion #2
1
Dx = v0t + at 2
2
Equation of Motion #3
v 2 = v02 + 2aDx w = w0 + 2aDq
1
Dq = w 0t + at 2
2
2
*Note: The x in
rotational
motion means
position on the
circle. More
generally the
equation is
written s=rθ
and in fact all of
the linear and
rotational
motion
equations would
use an s for
displacement in
its most general
form.
2
Extra Credit: Use the equations for rotational position,velocity & acceleration to convert
the Linear Equations of Motion into the Rotational Motion Equations.
#9 CENTER OF MASS LAB ACTIVITY
1. Find the center of mass of a 100 g mass at the 75 cm mark and a
200 g mass at the 25 cm mark. Will there be a net Torque associated
with this center of mass? Calculate the net Torque at the center of
mass.
2. Take a 20g and 40g mass. If the pivot point is at the
50 cm mark on the ruler and the 20g mass is placed at
the 70 cm mark, where should you put the 40g mass to
make the center of mass hit the pivot point. Calculate,
then check your work by testing out your calculated
position.
3. Take a 10 g mass. Place the 10g mass on the 80 cm
mark. Where should you make the pivot point so that it
touches the center of mass and the ruler balances?
Calculate then test with a ruler and masses.
4. A 100 g mass is at the 90cm mark on a ruler that
pivots at the 50 cm mark. A 500 g mass is at the 30 cm
mark on the same ruler. Where would a 200 g mass
need to be placed to make the center of mass hit the
50 cm mark. Calculate then verify.
TAP#8 & #9 & #10 & #11 SEE SHEET
ROTATIONAL MOTION OF TUMBLEBUGGY ACTIVITY
#12
We understand the linear motion of a tumblebuggy, but lets also describe the angular
component of motion on the tumblebuggy.
1) Find the speed of the tumblebuggy.
2) Find the angular speed of each of the tumblebuggy wheels.
3) Find the frequency and period of rotational of the tumblebuggy tires.
4) How many rpm’s does the tumblebuggy produce?
5) Write a paragraph explaining how you might attempt to find the torque produced
by the wheels. Include the information and the devices you would need to use in
order to measure it.
#13 ANGULAR ACCELERATION LAB
You will revisit the motion of objects accelerating down a ramp.
Engage: Golf Ball vs Marble Rotational Motion Racing Match
-Predict: Will a golf ball or a marble contain a greater angular acceleration? Will
their final linear velocities be the same or different?
Test: Your Objective is to compare the angular acceleration and final velocity of a golf
ball vs. the marble.
Object
Mass
(kg)
distanc
e (m)
time1
(s)
time2
(s)
time3(s)
tave(s)
radius (
r)
final
velocity
(m/s)
final
angular
velocity
(rad/s)
linear
acceler
ation
(m/s2)
angular
acceler
ation
(rad/s2)
Marble
Golf Ball
Interpret: What are your results? Do they seem reasonable? Explain the physics in a
paragraph.
#14 ANGULAR ACCELERATION LAB
1a. Predict which dowel has more rotational inertia?
1b. Predict Which ball has more
2. Test Each Prediction
3. Gradually reduce the radius of the circle that the golf and ping pong ball make. Is
it easier or harder to spin? is the rotational inertia bigger or smaller for smaller
radius’s?
4. Find the rotational inertia of each object using the formulas on the back of your
new sheet. I ball on string= mr2
Idowel = ½ mr2
m
Fat Dowel
Skinny Dowel
Ping Pong Ball
Golf Ball
r
#15 ROTATIONAL INERTIA BY ROLLING LAB
Theory: When an object rolls, it has kinetic energy both in its linear (translational) motion and its rotation. The distribution of the mass
about the body can affect how much energy is required to cause the spin. For example, a cart with very small wheels has almost
none of its kinetic energy distributed in rolling whereas a thin hoop has a large share of its mass moving at the radial distance. In the
case of an object rolling down a ramp from rest, the Total Kinetic Energy is equal to the change in gravitational potential energy
ΔU=mgΔh. The total kinetic energy of a body is found by Ktotal=Ktrans+Krot=1/2 mv2+ ½ Iω2
v0=0
d
v=rω
h1
h2
The new symbols, I and ω, are rotational inertia and angular velocity, respectively. Where I is a constant for rigid bodies and
depends on how the mass is distributed, it is usually stated as CmR2 where C is a constant between zero and 1. Angular velocity is
easily found by measuring the objects velocity and converting by the formula V=Rω.
Procedure: Raise a table on one side by putting a block of wood or a book under two of its legs. Allow objects of various shapes and mass
distributions to roll a distance of 1.5 meters across the tilted surface. The change in height is easily measured by comparing h1 to h2 as shown.
Timing the journey allows one to calculate the average translational speed, and from that the angular speed. Vaverage=1/2 (V+V0). The higher
rotational inertias become evident when more energy is in the rotation. This causes a slower translational verlocity and a longer rolling time.
Data: Start by measuring 1.5 m on the table top.
those 1.5 m.
Raise the table with the wood blocks and determine the change the height over
Δh=_________ m
Time the cart as it travels through this distance, fill in the chart
on the next page. *** Repeat your trials until the time value is
reliable.
As you do the trials make sure to predict whether the object will roll
faster or slower than the previous object. DO AT LEAST 4
Objects
mass
Radius
d (m)
hot wheel
1.5
blue cart
1.5
tape
cylinder
1.5
cap cylinder
1.5
solid squish
ball
1.5
ping pong
ball
1.5
marble
1.5
solid foam
disk
1.5
thick dowel
1.5
think dowel
1.5
time (s)
Vave=d/t
Vf=2Vavg
ω=vf/R
Ktotal=
mgΔh
Ktrans=
½ mv2
Krot=
Ktot-Ktrans
Rot. Inertia:
Krot/2ω2
C=
I/(mR2)
Analysis
1. Create a list that Organizes the objects in order of rotational inertia, from largest to smallest.
2. Use conservation of energy to show that neither mass nor radius is needed to predict the final velocity.
3. Is #2 verified by experiment? For example, do both solid cylinders have the same roll time?
4.
Can you understand that a disc is a solid cylinder and that a ring is a hollow cylinder?
5.
Do rings and cylinders have the same fall time? Do disks and rings have the same fall time? #2 & #4 suggest they
shoul.
6.
Expected values for C are 1 ring/hoop/tube, ½=disc/cylinder, 2/5 solid sphere, 2/3=hollow sphere. How well (in
percent) do your values match these expected values?
7.
What would roll down a hill faster, a hard-boiled egg, a fresh egg, or a hollow plastic Easter egg? Explain.
8.
Imagine you are at the store buying foods in cans. Would chicken broth roll down a hill faster than an empty can?
What about pumpkin pie mix (sticky & thick)?
9.
What was cart the fastest object today?
4.
An object that is at rest, not spinning, will not spin unless acted on by an outside torque. Knowing that a torque is a
force that acts at a radius, what force was causing the torque? What made the objects spin? If this force was absent
what would their movement be like?
5.
What are the likely sources of error that could make our measurement unreliable? How well did the experiment work (
see#6) Write a conclusion.