Rotational Inertia

Overview

Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA

Inertia is the resistance of an object to being accelerated. In linear kinematics, this concept is directly related to the mass of an object. The more massive an object, the more force is required to accelerate that object. This is seen directly in Newton's second law, which states that force is equal to mass times acceleration.

For rotation, there is a similar concept called rotational inertia. In this case, rotational inertia is the resistance of an object to being rotationally accelerated. Rotational inertia is dependent not only upon mass, but also upon the distance of mass from the center of rotation.

The goal of this experiment is to measure the rotational inertia of two rotating masses and to determine the dependence upon mass and distance from the axis of rotation.

Procedure

1. Measure the moment of inertia of the long rod.

Wind the string attached to the weight until the weight is near the spinning arm.
Drop the weight and measure the time it takes to drop, as well as the distance it drops.
Perform step 1.2 three times and calculate the average moment of inertia using Equation 7.
Compute the theoretical moment of inertia of the spinning rod using the following formula: .css-f1q1l5{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:flex-end;-webkit-box-align:flex-end;-ms-flex-align:flex-end;align-items:flex-end;background-image:linear-gradient(180deg, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 0.8) 40%, rgba(255, 255, 255, 1) 100%);width:100%;height:100%;position:absolute;bottom:0px;left:0px;font-size:var(--chakra-fontSizes-lg);color:#676B82;}
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Results

	Theoretical Value (kg m²)	Experimental Value (kg m²)	Difference (%)
Part 1	0.20	0.22	10
Part 2	0.08	0.07	14
Part 3	0.02	0.02< Log in or to access full content. Learn more about your institution’s access to JoVE content here Application and Summary Have you ever wondered why a tightrope walker carries a very long pole? The reason is that the long pole has a very large moment of inertia due to its length. Therefore, it requires a large amount of torque to make it rotate. This helps the tightrope walker to stay balanced, as the pole will remain steady. Wheels of cars and bicycles are never just solid disks; instead, they have spokes that support the wheel from the axle. This allows for a lighter design, which aids with speed, Howev Log in or to access full content. Learn more about your institution’s access to JoVE content here Tags Rotational Inertia Torque Rotational Acceleration Inertia Mass Linear Kinematics Force Rotational Kinematics Center Of Rotation Distance Formula Rotating Object System Experimental Set up Laws Equations Axle Axis Of Rotation Weight String 1. Measure the moment of inertia of the long rod. Wind the string attached to the weight until the weight is near the spinning arm. Drop the weight and measure the time it takes to drop, as well as the distance it drops. Perform step 1.2 three times and calculate the average moment of inertia using Equation 7. Compute the theoretical moment of inertia of the spinning rod using the following formula: , where is the mass of the rod and is the length. Compare the theoretical value with the measured value and record the difference. 2. Two masses attached to the rod. Place two 100-kg masses 20 cm away from the center of the rod. Repeat steps 1.2 and 1.3 with the attached masses. The total moment of inertia should be equal to the moment of inertia of the attached masses plus the moment of inertia of the rod. Use this fact, the results from step 1, and Equation 8 to determine the theoretical and experimental moments of inertia for the attached masses. Compare the theoretical values with the measured values and record the differences. 3. Effect of distance on moment of inertia. Repeat step 2 of the lab, but move the attached masses to 10 cm away from the center of rotation. Note any changes in the falling of the weight or the spinning of the rod. Compare the theoretical values with the measured values and record the differences. 4. Effect of mass on the moment of inertia. Repeat step 2 of the lab, but change the mass size to 200 kg. Compare the theoretical values with the measured values and record the differences. Skip to... 0:03 Overview 1:24 Principles Behind the Rotational Inertia Experiment 3:29 Moment of Inertia of a Rod 4:03 Moment of Inertia with Masses Attached to the Rod 5:34 Calculation and Results 6:35 Applications 7:27 Summary Videos from this collection: Now Playing Rotational Inertia Physics I 43.3K Views Newton's Laws of Motion Physics I 74.9K Views Force and Acceleration Physics I 78.3K Views Vectors in Multiple Directions Physics I 181.8K Views Kinematics and Projectile Motion Physics I 72.0K Views Newton's Law of Universal Gravitation Physics I 189.8K Views Conservation of Momentum Physics I 43.0K Views Friction Physics I 52.5K Views Hooke's Law and Simple Harmonic Motion Physics I 61.0K Views Equilibrium and Free-body Diagrams Physics I 37.2K Views Torque Physics I 24.0K Views Angular Momentum Physics I 35.6K Views Energy and Work Physics I 49.4K Views Enthalpy Physics I 59.5K Views Entropy Physics I 17.5K Views Privacy Terms of Use Policies Contact Us Recommend to library JoVE NEWSLETTERS Research JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive Education JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site Authors Overview Publishing Process Editorial Board Scope and Policies Peer Review FAQ Submit Librarians Overview Testimonials Subscriptions Access Resources Library Advisory Board FAQ ABOUT JoVE Overview Leadership Blog JoVE Help Center Copyright © 2025 MyJoVE Corporation. All rights reserved