Warm Up
AP PHYSICS
MONDAY 15.03.09
STANDARDS:
Week 27
Find the rpm of a tire that rotates with
a period of 0.04s.
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 gain experiential
understanding of the concept of angular
velocity by completing the 5 lab tasks as
a precursor to understanding angular
momentum.
Agenda:
1. Warm Up
2. Review HW Tap#9Stamp HW
3. Review PreLab for Lab#11
4. Lab #11 Angular Motion Experience Lab
5. Tap#11 Calculations & conversions using angular
motion quantities
Homework
Tap#10
AP PHYSICS
TUESDAY 15.03.10
STANDARDS:
Warm Up
Compare and contrast linear velocity
and angular velocity.
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 explain the
similarities and differences between
rotational motion and linear motion
Agenda:
1. Warm Up
2. Review Lab 11 & HW 11
3. Collect HW up to Tap#9 tomorrow
4. Mini Lecture: rotational vs Linear
5. Tumblebuggy Revisited #12
Homework
Tap#11 Converting Problems
AP PHYSICS
WEDNESDAY 15.03.04
E-Effective Communicators
Warm Up
A car with 60.0 cm rims is moving ahead at a
speed of 12.0 m/s. Find the angular speed,
period, and frequency of the tires.
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 use the rotational
equations of motion to find the angular
acceleration of a marble rolling down the
ramp.
Agenda:
1. Warm Up
2. #13 Golf ball vs Marble
Homework
Tap#12
AP PHYSICS
THURSDAY 15.03.12
STANDARDS:
P-Problem Solvers
Warm Up
A 0.002 m radius marble accelerates at
2m/s2 down a ramp for 1.4 seconds. If it
starts at rest, what is its final angular
velocity?
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 use the rotational
equations of motion to find the angular
acceleration of a marble rolling down the
ramp.
Agenda:
1. Warm Up
2. Rotational Acceleration of a marble Lab
Homework
Tap #13
Rotational Motion Quiz
Tomorrow (not ap questions)
AP PHYSICS
FRIDAY 15.03.06
Warm Up
Free Day
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 understand the
factors affecting the motion of objects
moving translationally and rotationally.
Agenda:
1. Warm Up
2. Finish Acceleration Lab
3. Take Angular Motion Quiz
Homework
Tap#13
TAP#2
A. F=100 N B. F=20 N
r=50m
r=20m
τ=?
θ=30°
τ=?
F
C.
F=10N
θ
r=4N
θ=40°
r
D.
F=10N
r=4N
Φ=40°
Φ
F
r
1.
(1) The nests built by the mallee fowl of Australia can have masses as large as
3.00x105kg. Suppose a nest with this mass is being lifted by a crane. The
boom of the crane makes an angle of 45.0° with the ground. If the axis of
rotation is the lower end of the boom at point A, the torque produced by the nest
has a magnitude of 3.20x107Nm. Treat the boom’s mass as negligible, and
calculate the length of the boom.
2.
(3) A meterstick of negligible mass is fixed horizontally at its 100.0 cm mark.
Imagine this meterstick used as a display for some fruits and vegetables with
record-breaking masses. A lemon with a mass of 3.9 kg hangs from the 70.0
cm mark, and a cucumber with a mass of 9.1 kg hangs from the x cm mark.
What is the value of x if the net torque acting on the meterstick is 56.0 Nm in
the counterclockwise direction?
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.
TAP#3 TORQUE& EQUILIBRIUM
A.
F=6N
r=8N
θ=20°
r
θ
F
B.
Fap=20N
l=10m
r=3m
τnet=?
mrod=5kg
mblock=2kg
Fap
l
r
mrodg
r
1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where
should one hang a mass of 0.50 kg to balance a stick? -- 36 cm
2. A meterstick of negligible mass has a screw drilled in it at the 0.60 m mark so it
is free to spin. If the meterstick is stuck into the wall and a 2.0 kg mass hung at
the 0m mark while you are holding up the other side, what is the magnitude of
the net torque on the meterstick about the fulcrum immediately after you release
the meterstick?
TAP #4 TORQUE WORKSHEET PROVIDED TO
YOU TAP#5 CENTER OF MASS
#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.
#10 TORQUE ON A HINGE JOINT
Spring Scale
h
T
m
Hinge
M
R
L
Theory
Torque is a force at a radius. Specifically a torque (twist) is caused when a force is applied perpendicular to a radius. The Greek letter τ, tau, is used for torque.
Torques can act clockwise and counterclockwise and thus torque is a vector. The vector sum of all the torques on a system is called a net torque. The formula
for any single torque is τ=r x F or |τ|=r Fperpendicular where only the perpendicular component of the force causes a torque.
Apparatus Details
The set up illustrated above is a system of variable torque. However, since rotational will not occur, the net torque will be 0 in all cases. For simplicity, we will
agree to assign the hinge (pivot) as the zero point. On the diagram at right, draw labeled vector arrows for the three forces causing torques: the weight of the
mass M, the weight of the plank m, and the Tension T. There is another force on the plank; it is the normal force from the hinge. Can you convince yourself that
(if you were to draw it) it would point up and to the right?
Both weights’ torques point downward (clockwise), the tension’s point upward (counterclockwise). However, the tension is not straight up. Since only
perpendicular force can cause a torque, draw and label sine and cosine components of the tension. Label each component.
Questions
i According to the figure on the left, what is the torque from the hanging mass, M
ii.
What is the torque from the plank’s mass?
iii.
What is the torque from the rope’s tension?
iv.
Can you prove that the normal force provides no torque?
v.
Which is the larger? The torque from the two masses, or the rope’s? Explain.
TAP#6 TORQUE ON A HINGE JOINT
Spring Scale
A.
T
30cm
80g
Hinge
500g
40cm
50cm
This is a setup that may be given on the AP Test so lets get to know it.
1.
Find the Center of Mass of this 2 mass system.
2.
Find the Torque caused by the the uniform density hinged rod.
3.
Find the Torque caused by the hanging mass.
4.
Find the Torque caused by the Rope.
5.
Find the angle between the rope and the hinged rod
6.
Find the component of Tension that causes Torque
7.
Find the component of Tension that is wasted (that does not produce Torque)
8.
Find the Tension reading on the spring scale.
9.
Give yourself a pat on the back for finishing!!!
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.