TABLE 10.2 Moments of Inertia of Homogeneous Rigid Objects with Different Geometries Ноор or thin cylindrical shell IM = MR² Long, thin rod with rotation axis through center IM ML 12 Solid sphere M = MR Solid cylinder or disk Long, thin rod with rotation axis through end 1=- ML? ICM MR Thin spherical shell IM =2 MR² R. Hollow cylinder Rectangular plate lom = M(R," + R") kM = M(a + t®) TABLE 18.1 Average Expansion Coefficients for Some Materials Near Room Temperature Average Linear Expansion Coefficient (a)(°C)-1 Average Volume Еxpansion Coefficient (B)('C)-1 Material Material (Solids) (Liquids and Gases) Aluminum 24 x 10-6 Acetone 1.5 x 10-4 Brass and bronze 19 x 10-6 Alcohol, ethyl 1.12 x 10-4 12 x 10-6 17 x 10-6 Concrete Benzene 1.24 x 10-4 Copper Glass (ordinary) Glass (Pyrex) Invar (Ni-Fe alloy) Gasoline 9.6 x 10-4 9 x 10-6 Glycerin Mercury Turpentine 4.85 x 10-4 1.82 x 10-4 3.2 x 10-6 0.9 x 10-6 9.0 x 10-1 3.67 x 10-3 3.665 x 10-3 Lead 29 x 10-6 Air' at 0°C Steel 11 x 10-6 Helium *Gases do not have a specific value for the volume expansion coefficient because the amount of expansion depends on the type of process through which the gas is taken. The values given here assumc the gas undergoes an expansion at constant pressure.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Consider an object with any one of the shapes displayed as shown. What is the percentage increase in the moment of inertia of the object when it is warmed from 0°C to 100°C if it is composed of (a) copper or (b) aluminum?
Assume the average linear expansion coefficients as shown do not vary between 0°C and 100°C. (c) Why are the answers for parts (a) and (b) the same for all the shapes?

TABLE 10.2 Moments of Inertia of Homogeneous Rigid Objects with Different Geometries
Ноор or thin
cylindrical shell
IM = MR²
Long, thin rod
with rotation axis
through center
IM
ML
12
Solid sphere
M = MR
Solid cylinder
or disk
Long, thin
rod with
rotation axis
through end
1=- ML?
ICM
MR
Thin spherical
shell
IM =2 MR²
R.
Hollow cylinder
Rectangular plate
lom = M(R," + R")
kM = M(a + t®)

TABLE 18.1 Average Expansion Coefficients for Some Materials Near Room Temperature
Average Linear
Expansion
Coefficient
(a)(°C)-1
Average Volume
Еxpansion
Coefficient
(B)('C)-1
Material
Material
(Solids)
(Liquids and Gases)
Aluminum
24 x 10-6
Acetone
1.5 x 10-4
Brass and bronze
19 x 10-6
Alcohol, ethyl
1.12 x 10-4
12 x 10-6
17 x 10-6
Concrete
Benzene
1.24 x 10-4
Copper
Glass (ordinary)
Glass (Pyrex)
Invar (Ni-Fe alloy)
Gasoline
9.6 x 10-4
9 x 10-6
Glycerin
Mercury
Turpentine
4.85 x 10-4
1.82 x 10-4
3.2 x 10-6
0.9 x 10-6
9.0 x 10-1
3.67 x 10-3
3.665 x 10-3
Lead
29 x 10-6
Air' at 0°C
Steel
11 x 10-6
Helium
*Gases do not have a specific value for the volume expansion coefficient because the amount of expansion depends
on the type of process through which the gas is taken. The values given here assumc the gas undergoes an expansion
at constant pressure.

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