Lab
Rotational Inertia
Printer Friendly Version
In this lab we will be using the Rotational Inertia Demonstrator made by Arbor Scientific.
This device has a central, low friction, pulley with three different radii from which strings can be tied. It also has four thin rods that form spokes on which masses can be placed at virtually any desired position.
The moment of inertia of the central pulley, independent of the four rods and their moveable masses, is given by the manufacturer as 0.00058 kg m
^{2 }
. All other measurement will be taken as the experiment is completed.
In each experiment, we will ultimately be calculating the moment of inertia of the pulley and its moveable masses. We will deal with rotational (angular) kinematics properties and their relationship to linear (translational or tangential) properties of a falling mass as well as potential gravitational energy, translational kinetic energy, and rotational kinetic energy.
Refer to the following information for the next four questions.
Before we collect any further data, we need to take measurements that will allow us to directly calculate the moment of inertia of the entire pulley assembly: central pulley, rods, and moveable masses.
mass of a single rod (in kg)
length of a single rod measured from the center of the pulley (in meters)
mass of a single moveable mass (in kg)
radius of the moveable masses measured from the center of the pulley (in meters)
Refer to the following information for the next question.
Phase I. In this part of the experiment we will wrap the string around the smallest radius of the pulley, 0.0202 meters.
What is the mass (in kg) of the hanging mass?
You will complete three trials using a motion detector as well as the rotational inertia demonstrator. From each trial you need to record the initial time, initial height, final time, and final height. Then you will calculate the time interval and the distance required for the mass to reach the ground.
initial time
initial height
final time
final height
time interval
distance
linear acc
Trial
(sec)
(meters)
(sec)
(meters)
(sec)
(meters)
(m/sec
^{2}
)
1
2
3
Analysis of first radius
What was the average linear acceleration of your falling mass for all three trials?
Which trial's acceleration came closest to this value?
1
2
3
For the remaining calculations in this section, use the data for the acceleration, time interval spent falling, and the distance fallen from the trial chosen in the previous question.
Calculate the final linear velocity of the falling mass in m/sec.
Calculate the initial potential gravitational energy of the falling mass in Joules.
Calculate the final translational kinetic energy of the falling mass in Joules.
Calculate the final angular velocity of the pulley with its rods and moveable masses in rad/sec.
Refer to the following information for the next question.
Phase II: In this part of the experiment we will wrap the string around the largest radius of the pulley, 0.03852 meters.
You will complete three trials using a motion detector as well as the rotational inertia demonstrator. From each trial you need to record the initial time, initial height, final time, and final height. Then you will calculate the time interval and the distance required for the mass to reach the ground.
initial time
initial height
final time
final height
time interval
distance
linear acc
Trial
(sec)
(meters)
(sec)
(meters)
(sec)
(meters)
(m/sec
^{2}
)
1
2
3
Analysis of second radius
What was the average linear acceleration of your falling mass for all three trials?
Which trial's acceleration came closest to this value?
1
2
3
For the remaining calculations in this section, use the data for the acceleration, time interval spent falling, and the distance fallen from the trial chosen in the previous question.
Calculate the final linear velocity of the falling mass in m/sec.
Calculate the initial potential gravitational energy of the falling mass in Joules.
Calculate the final translational kinetic energy of the falling mass in Joules.
Calculate the final angular velocity of the pulley with its rods and moveable masses in rad/sec.
Refer to the following information for the next eleven questions.
Data Analysis
For the first radius, what was the pulley's angular acceleration in rad/sec
^{2}
?
For the first radius, what was the tension, in N, in the string as the mass was falling?
For the first radius, what was the torque, in mN, produced by the tension in the string as the mass was falling?
For the first radius, what was the experimental moment of inertia, in kg m
^{2}
of the complete pulley assembly?
For the first radius, what was the final rotational KE, in J, of the pulley with its rods and moveable masses?
For the second radius, what was the pulley's angular acceleration in rad/sec
^{2}
?
For the second radius, what was the tension, in N, in the string as the mass was falling?
For the second radius, what was the torque, in mN, produced by the tension in the string as the mass was falling?
For the second radius, what was the experimental moment of inertia, in kg m
^{2}
of the complete pulley assembly?
For the second radius, what was the final rotational KE, in J, of the pulley with its rods and moveable masses?
Based on the data collected on the thin rods and moveable masses, what should have been the theoretical moment of inertia, in kg m
^{2}
, for your complete pulley assembly?
Refer to the following information for the next four questions.
At this point we are now ready to make some conclusions regarding our values. The Law of Conservation of Energy states that mechanical energy sould be conserved in a system in the absence of friction. In our trials, we would compare the gravitational potenial energy of the falling mass at the start of a trial to the total kinetic energy of the mass and the rotating pulley at the end of the trial.
For the small radius, what was your value for the sum of the two final kinetic energies: KE
_{translational}
+ KE
_{rot}
?
For the large radius, what was your value for the sum of the two final kinetic energies: KE
_{translational}
+ KE
_{rot}
?
Which radius had the closest match to the original PE of the mass?
small
large
both matched equally well
Did this experiment confirm that mechanical energy is conserved in a frictionless system? Elaborate.
Refer to the following information for the next three questions.
In each set of trials, you were asked to calculate the moment of inertia of the complete pulley assembly. We also calculated the theoretical moment of inertia by measuring the masses of the thin rods and moveable masses as well as their lengths and radii. You are now going to calculate three errors for your experiment.
What was your average experimental value for the moment of inertia of the complete pulley assembly?
Calculate a percent difference between the two experimental values.
Calculate a percent error between your average expeimental value and the calculatd value for the moment of inertia.
Related Documents
Lab:
Labs -
A Battering Ram
Labs -
A Photoelectric Effect Analogy
Labs -
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Labs -
Air Track Collisions
Labs -
Ballistic Pendulum
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Bouncing Steel Spheres
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Energy and Vertical Circles
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Density of an Unknown Fluid
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Loop-the-Loop
Labs -
Mass of a Paper Clip
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Ramps: Sliding vs Rolling
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rube Goldberg Challenge
Labs -
Spring Carts
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Video Lab: Blowdart Colliding with Cart
Labs -
Video LAB: Circular Motion
Labs -
Video Lab: M&M Collides with Pop Can
Labs -
Video Lab: Marble Collides with Ballistic Pendulum
Resource Lesson:
RL -
A Chart of Common Moments of Inertia
RL -
A Further Look at Angular Momentum
RL -
APC: Work Notation
RL -
Center of Mass
RL -
Centripetal Acceleration and Angular Motion
RL -
Conservation of Energy and Springs
RL -
Discrete Masses: Center of Mass and Moment of Inertia
RL -
Energy Conservation in Simple Pendulums
RL -
Gravitational Energy Wells
RL -
Hinged Board
RL -
Introduction to Angular Momentum
RL -
Mechanical Energy
RL -
Momentum and Energy
RL -
Potential Energy Functions
RL -
Principal of Least Action
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
RL -
Rotational Kinematics
RL -
Rotational Kinetic Energy
RL -
Springs and Blocks
RL -
Symmetries in Physics
RL -
Tension Cases: Four Special Situations
RL -
Thin Rods: Center of Mass
RL -
Thin Rods: Moment of Inertia
RL -
Torque: An Introduction
RL -
Work
RL -
Work and Energy
Worksheet:
APP -
The Baton Twirler
APP -
The Jogger
APP -
The Pepsi Challenge
APP -
The Pet Rock
APP -
The Pool Game
APP -
The See-Saw Scene
CP -
Center of Gravity
CP -
Conservation of Energy
CP -
Momentum and Energy
CP -
Momentum and Kinetic Energy
CP -
Power Production
CP -
Satellites: Circular and Elliptical
CP -
Torque Beams
CP -
Torque: Cams and Spools
CP -
Work and Energy
NT -
Center of Gravity
NT -
Center of Gravity vs Torque
NT -
Cliffs
NT -
Elliptical Orbits
NT -
Escape Velocity
NT -
Falling Sticks
NT -
Gravitation #2
NT -
Ramps
NT -
Rolling Cans
NT -
Rolling Spool
NT -
Satellite Positions
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Energy/Work Vocabulary
WS -
Force vs Displacement Graphs
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
Moment Arms
WS -
Moments of Inertia and Angular Momentum
WS -
Potential Energy Functions
WS -
Practice: Momentum and Energy #1
WS -
Practice: Momentum and Energy #2
WS -
Practice: Uniform Circular Motion
WS -
Practice: Vertical Circular Motion
WS -
Rotational Kinetic Energy
WS -
Static Springs: The Basics
WS -
Torque: Rotational Equilibrium Problems
WS -
Work and Energy Practice: An Assortment of Situations
WS -
Work and Energy Practice: Forces at Angles
TB -
Basic Torque Problems
TB -
Center of Mass (Discrete Collections)
TB -
Moment of Inertia (Discrete Collections)
TB -
Rotational Kinematics
TB -
Rotational Kinematics #2
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2020
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton