Lab 10 Report

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School

Florida International University *

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Course

2048L

Subject

Mechanical Engineering

Date

Dec 6, 2023

Type

docx

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Uploaded by BrigadierSquidMaster940

Lab 9 Lab Partners: Title: Conservation of Angular Momentum & Rotational Dynamics Preliminary Questions: 1, Mass is a measure of the amount of matter in an object and is constant, while moment of inertia depends on the distribution of mass relative to the axis of rotation. They do not have the same dimensions. 2, The total moment of inertia of a system of several objects rotating together is the sum of the individual moments of inertia of each object. 3, - Point mass (m) rotating at a distance (r) from the axis of rotation: I = mr 2 - Thin rod of length (L) rotating about its central axis: I = 1 12 m* L 2 - Solid disk of radius (R) rotating about its central axis: I = 1 12 m* R 2 - Annular disk (disk with a hole in the middle) with inner radius (r1) and outer radius (r2): I = 1 12 m * (r1 2 + r2 2 ) Analysis: PI

1, Aluminum Disk 1: I = mr 2 2 → I = ( 0.106 )( 0.045 ) 2 → 0.0024 kg m 2 Aluminum Disk 2: I = mr 2 2 → I = ( 0.106 )( 0.045 ) 2 → 0.0024 kg m 2 Steel Disk: I = 1 2 mR 2 r 2 → 1 2 (0.277)(0.0130) 2 (0.045) 2 → 0.0003 kg m 2 2, Aluminum Disk (Run 1): α = − 0.08421 7.5 = −0.011228 rad/s Steel Disk (Run 4): α = 1.299 7.5 = 0.1732 rad/s The negative angular acceleration of the aluminum disk suggests external forces opposing its initial motion, causing a decrease in angular velocity. In contrast, the positive angular acceleration of the steel disk indicates external forces supporting its initial motion, resulting in an increase in angular velocity. In summary, the aluminum disk is slowing down, while the steel disk is speeding up, as explained by the differing signs and magnitudes of angular acceleration. 3, Run 2: α acceleration = − 1.230 4 = -0.3075 rad/S2 4, Before: α = 49 rad/s | After: α = 22 rad/s | ΔT = 0.40 s 5, Angular momentum before = L = I ω = (1.060*10 -4 ) (49) = 5.2*10 -3 kgm 2 /s Angular momentum after = L = I ω = (1.060 + 1.05) *10 -4 (22) = 5.3*10 -3 kgm 2 /s Percent Difference = 2% 6, The entire difference in angular speed before and after increasing the mass can be attributed to frictional losses. Since friction is the sole force acting on the system capable of influencing angular velocity, any observed changes in ω are a direct result of friction's impact on the system's motion.

PII 1, Acceleration decreases as distance increases. 2, TA had derived the equation in which the equation is in y = mx + b 3, Graph is shown below 4, The slope of the graph is -0.1016. The slope is the rate of change in the measured quantity for each unit change in mass. The slope is negative, which suggests that there is a negative correlation between the measured quantity and the mass of the cylindrical mass, which isn’t what we wanted to get. M = 0.1016/2 = 0.0508 kg Percent Difference = 0.08 – (0.0508) / 0.08 (*100%) = 36% (However we did get a negative value for our slope)

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