# Experiment 8.1 and 8.2.docx - Joshua Tashbar Lab Date...

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Joshua Tashbar Lab Date: 3-16-17 Report Date: 3-19-17 Lab Instructor: Shen Li Qiu TA: Giouli Galanakou Title of experiments: Experiment 8.1 Rigid-body rotation about a moving axis & Experiment 8.2 Moment of inertia Lab Section: Thursdays 10am, 018 The purpose of experiment 8.1 was to study how rigid-body rotation about a moving axis works. The purpose of experiment 8.2 was twofold: 1. Measure the moments of inertia of rigid bodies: disk, ring and thin-walled- hollow sphere 2. Compare the measured and the calculated moments of inertia to determine the c values of the moments of inertia of the rigid bodies.
The moments of inertia of the round rigid bodies shown in the previous page can be expressed as: I = cM R 2 Where c = 2 5 for solid sphere, c = 1 2 for solid cylinder and disk, c = 2 3 for thin-wall hollow sphere, and c = 1 for thin-wall hollow cylinder The question that must be asked and answered is: If you race various round rigid bodies by releasing them from the top of an inclined place, which of them will reach the bottom of the inclined plane first? The most vitally important key to answering this question is by using the concept of “rigid-body rotation about a moving axis”. This concept states that every possible motion of a rigid body can be represented as a combination of translational motion of the center of mass and rotation about an axis though the center of mass. This means that the kinetic energy of a rigid body is: K = 1 2 M v cm 2 + 1 2 I cm ω 2 ( 1 ) Where M , v cm ,I cm are the mass, speed of the center of the mass, moment of inertia and angular speed of the rigid body, and ω = v cm R if the rigid body rolls along a plane without slipping. The total mechanical energy of the rigid body is conserved: K 1 + U 1 = K 2 + U 2 ( 2 ) Because: i. No work is done by kinetic friction if the rigid body which rolls along a plane without slipping. ii. The effect of rolling friction can be ignored provided that the body and the surface on which it rolls are perfectly rigid.
Thus by i. and ii. only the conservative force of gravity does work on the rigid body. (which for