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Rotational Inertia

Panoramica

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.

Procedura

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

  1. Wind the string attached to the weight until the weight is near the spinning arm.
  2. Drop the weight and measure the time it takes to drop, as well as the distance it drops.
  3. Perform step 1.2 three times and calculate the average moment of inertia using Equation 7.
  4. Compute the theoretical moment of inertia of the spinning rod using the following formula: Equation 25.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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Risultati
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<

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Tags
Rotational InertiaTorqueRotational AccelerationInertiaMassLinear KinematicsForceRotational KinematicsCenter Of RotationDistanceFormulaRotating ObjectSystemExperimental Set upLawsEquationsAxleAxis Of RotationWeightString

Vai a...

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

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