Lab
Moment of Inertia of a Bicycle Wheel
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Purpose
The purpose of this lab is to have students investigate the rotational inertia of a suspended bicycle wheel. The use of a motion detector and data analysis techniques will show the relationship between the variables for the falling mass and its acceleration.
Laboratory set-up
Each group of three students will need the following equipment:
1 suspended bicycle wheel with a string securely wrapped along its circumference
1 50-gram mass hanger
1 set of slotted masses
1 LabPro
1 motion detector
First verify that the string attached to your bicycle wheel is securely attached and has a loop at the end to hold the mass hanger. Next, unroll about one meter of string, place the mass hanger on the end of the string and then hold the rim of the wheel stationary so that you can position the motion detector on the floor as shown in the diagram below.
diagram courtesy of Daniel Weaver (c/o 2008)
When you think everything is aligned, one student should start LoggerPro 3.1. With the motion detector properly connected, the program should display graphs of position versus time and velocity versus time. When you are ready to obtain data, hit the
Collect
button on the top right-hand side of the program window and run a few test trials to make sure that the detector can "see" the bottom of the hanger as the wheel rotates and the hanger descends.
You will be watching for the classic parabolic position-time graph signifying that the hanger is accelerating in a negative direction as the string unwraps and it descends towards the ground. Once this graph has formed, stop collecting data.
To analyze your velocity-time graph highlight a central section of your parabola, click on the velocity-time graph, and the linear fit,
R=
, button in the top toolbar.
The acceleration for that trial will be displayed as the slope of your velocity-time graph. In this case it was -0.1105 m/s/s. Repeat each trial two times, taking the average as your final value for each mass.
Data Collection
mass
(grams)
trial 1
(m/sec
^{2}
)
trial 2
(m/sec
^{2}
)
average
(m/sec
^{2}
)
50
60
70
80
90
100
Data Analysis and Conclusions
We will now use EXCEL to graph
1/a vs 1/m
and data analysis techniques to determine the bicycle wheel's Moment of inertia. Open the file 1-bicycle.xls on the file system and input your data.
What is the equation of your line?
If the radius of the wheel is 0.28 meters, use the slope of your line to determine its moment of inertia.
If the mass of the wheel is 1.75 kg, what is the wheel's radius of gyration, k?
If the length of string was 1.5 meters and the hanger was released from a position of rest, use the data from your final trial to answer the following questions.
What was the average acceleration for your last trial?
Determine how fast the mass hanger was traveling at the end just as the mass hanger stopped falling and was jerked upwards.
Determine how fast the wheel was rotating just as mass hanger stopped falling and was jerked upwards.
What was the wheel's angular momentum just before the mass hanger stopped falling and was jerked upwards?
What was the total KE in the system (the wheel's rotational KE plus the mass hanger's linear KE) just before the mass hanger stopped falling and was jerked upwards?
What was the total PE in the system prior to the mass hanger's release?
Was energy conserved during this final trial? Why or why not?
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Resource Lesson:
RL -
A Chart of Common Moments of Inertia
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A Derivation of the Formulas for Centripetal Acceleration
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A Further Look at Angular Momentum
RL -
Accelerated Motion: A Data Analysis Approach
RL -
Accelerated Motion: Velocity-Time Graphs
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Analyzing SVA Graph Combinations
RL -
Average Velocity - A Calculus Approach
RL -
Center of Mass
RL -
Centripetal Acceleration and Angular Motion
RL -
Chase Problems
RL -
Chase Problems: Projectiles
RL -
Comparing Constant Velocity Graphs of Position-Time & Velocity-Time
RL -
Conservation of Energy and Springs
RL -
Constant Velocity: Position-Time Graphs
RL -
Constant Velocity: Velocity-Time Graphs
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Derivation of the Kinematics Equations for Uniformly Accelerated Motion
RL -
Derivation: Period of a Simple Pendulum
RL -
Derivatives: Instantaneous vs Average Velocities
RL -
Directions: Flash Cards
RL -
Discrete Masses: Center of Mass and Moment of Inertia
RL -
Energy Conservation in Simple Pendulums
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Freefall: Horizontally Released Projectiles (2D-Motion)
RL -
Freefall: Projectiles in 1-Dimension
RL -
Freefall: Projectiles Released at an Angle (2D-Motion)
RL -
Gravitational Energy Wells
RL -
Hinged Board
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Introduction to Angular Momentum
RL -
Kepler's Laws
RL -
LC Circuit
RL -
Magnetic Forces on Particles (Part II)
RL -
Monkey and the Hunter
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Period of a Pendulum
RL -
Properties of Friction
RL -
Rolling and Slipping
RL -
Rotary Motion
RL -
Rotational Dynamics: Pivoting Rods
RL -
Rotational Dynamics: Pulleys
RL -
Rotational Dynamics: Rolling Spheres/Cylinders
RL -
Rotational Equilibrium
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Rotational Kinematics
RL -
Rotational Kinetic Energy
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Springs and Blocks
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Springs: Hooke's Law
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Static Equilibrium
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Summary: Graph Shapes for Constant Velocity
RL -
Summary: Graph Shapes for Uniformly Accelerated Motion
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SVA: Slopes and Area Relationships
RL -
Symmetries in Physics
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Systems of Bodies
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Tension Cases: Four Special Situations
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The Law of Universal Gravitation
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Thin Rods: Center of Mass
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Thin Rods: Moment of Inertia
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Torque: An Introduction
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Uniform Circular Motion: Centripetal Forces
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Universal Gravitation and Satellites
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Universal Gravitation and Weight
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Vector Resultants: Average Velocity
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Vertical Circles and Non-Uniform Circular Motion
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What is Mass?
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Work and Energy
Review:
REV -
Review: Circular Motion and Universal Gravitation
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Big Al
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Big Fist
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Family Reunion
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Hackensack
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Ring Around the Collar
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The Antelope
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The Baseball Game
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The Baton Twirler
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The Big Mac
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The Box Seat
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The Cemetary
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The Golf Game
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The Jogger
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The Satellite
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The See-Saw Scene
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The Spring Phling
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Timex
CP -
2D Projectiles
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Center of Gravity
CP -
Centripetal Acceleration
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Centripetal Force
CP -
Dropped From Rest
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Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
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Force and Weight
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Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Freefall
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
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Inertia
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Mobiles: Rotational Equilibrium
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Net Force
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Newton's Law of Motion: Friction
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Non-Accelerated and Accelerated Motion
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Satellites: Circular and Elliptical
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Static Equilibrium
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Tensions and Equilibrium
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Torque Beams
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Torque: Cams and Spools
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Tossed Ball
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Up and Down
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Acceleration
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Air Resistance #1
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An Apple on a Table
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Apex #1
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Apex #2
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Average Speed
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Back-and-Forth
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Center of Gravity
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Center of Gravity vs Torque
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Circular Orbits
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Crosswinds
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Falling Rock
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Falling Spheres
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Falling Sticks
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Friction
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Frictionless Pulley
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Gravitation #1
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Head-on Collisions #1
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Head-on Collisions #2
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Headwinds
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Ice Boat
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Monkey Shooter
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Pendulum
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Projectile
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Rolling Cans
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Rolling Spool
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Rotating Disk
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Sailboats #1
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Sailboats #2
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Scale Reading
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Settling
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Skidding Distances
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Spiral Tube
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Tensile Strength
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Terminal Velocity
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Tug of War #1
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Tug of War #2
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Two-block Systems
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Accelerated Motion: Analyzing Velocity-Time Graphs
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Accelerated Motion: Graph Shape Patterns
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Advanced Properties of Freely Falling Bodies #2
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Advanced Properties of Freely Falling Bodies #3
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Average Speed Drill
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Basic Practice with Springs
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Calculating Force Components
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Chase Problems #2
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Chase Problems: Projectiles
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Combining Kinematics and Dynamics
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Constant Velocity: Converting Position and Velocity Graphs
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Constant Velocity: Position-Time Graphs #1
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Constant Velocity: Position-Time Graphs #2
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Constant Velocity: Position-Time Graphs #3
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Constant Velocity: Velocity-Time Graphs #1
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Constant Velocity: Velocity-Time Graphs #2
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Constant Velocity: Velocity-Time Graphs #3
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Converting s-t and v-t Graphs
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Distinguishing 2nd and 3rd Law Forces
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Energy Methods: More Practice with Projectiles
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Energy Methods: Projectiles
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Force vs Displacement Graphs
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Freebody Diagrams #1
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Freebody Diagrams #2
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Freebody Diagrams #3
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Freebody Diagrams #4
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Freefall #1
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Freefall #2
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Freefall #3
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Freefall #3 (Honors)
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Horizontally Released Projectiles #1
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Horizontally Released Projectiles #2
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Inertial Mass Lab Review Questions
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Introduction to Springs
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Kepler's Laws: Worksheet #1
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Kepler's Laws: Worksheet #2
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Kinematics Along With Work/Energy
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Kinematics Equations #1
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Kinematics Equations #2
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Kinematics Equations #3: A Stop Light Story
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Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
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Lab Discussion: Inertial and Gravitational Mass
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Moment Arms
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Moments of Inertia and Angular Momentum
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More Practice with SHM Equations
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net F = ma
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Pendulum Lab Review
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Pendulum Lab Review
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Position-Time Graph "Story" Combinations
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Practice: SHM Equations
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Practice: Uniform Circular Motion
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Practice: Vertical Circular Motion
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Projectiles Released at an Angle
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Ropes and Pulleys in Static Equilibrium
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Rotational Kinetic Energy
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SHM Properties
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Standard Model: Particles and Forces
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Static Springs: The Basics
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SVA Relationships #1
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SVA Relationships #2
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SVA Relationships #3
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SVA Relationships #4
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SVA Relationships #5
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Torque: Rotational Equilibrium Problems
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Universal Gravitation and Satellites
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Vertical Circular Motion #1
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Vocabulary for Newton's Laws
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Work and Energy Practice: An Assortment of Situations
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Work and Energy Practice: Forces at Angles
TB -
2A: Introduction to Motion
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2B: Average Speed and Average Velocity
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Antiderivatives and Kinematics Functions
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Basic Torque Problems
TB -
Center of Mass (Discrete Collections)
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Centripetal Acceleration
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Centripetal Force
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Honors: Average Speed/Velocity
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Kinematics Derivatives
TB -
Moment of Inertia (Discrete Collections)
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Projectile Summary
TB -
Projectile Summary
TB -
Projectiles Mixed (Vertical and Horizontal Release)
TB -
Projectiles Released at an Angle
TB -
Rotational Kinematics
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Rotational Kinematics #2
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Set 3A: Projectiles
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Systems of Bodies (including pulleys)
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Work, Power, Kinetic Energy
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