Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Compound objects. Moment of inertia is a scalar. There-fore, if several objects are connected together, the moment ofinertia of this compound object is simply the scalar (algebraic)sum of the moments, of inertia of each of the component. objects. Use this principle to answer each of the followingquestions about the moment of inertia of compound objects:(a) A thin uniform 2.50 $\mathrm{kg}$ bar 1.50 $\mathrm{m}$ long has a small1.25 $\mathrm{kg}$ mass glued to each end. What is the moment of inertiaof this object about an axis perpendicular to the bar through its center? (b) What is the moment of inertia of the object inpart (a) about an axis perpendicular to the bar at one end?(c) $A 725$ g metal wire is bent into the shape of a hoop 60.0 $\mathrm{cm}$in diameter. Six wire spokes, each of mass 112 g, are added from the center of the hoop to the rim. What is the moment ofinertia of this object about an axis perpendicular to it throughits center?

a) 1.875 $\mathrm{kg} \mathrm{m}^{2}$b) 0.1862 $\mathrm{kg} \mathrm{m}^{2}$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

Lectures

04:16

In mathematics, a proof is…

02:21

In physics, rotational dyn…

00:56

Calculate the moment of in…

02:40

A uniform disk of radius $…

03:57

Perpendicular-Axis Theorem…

02:36

02:04

01:00

The parallel axis theorem …

03:14

The moments and product of…

03:47

A solid circular disk has …

03:55

Two metal disks, one with …

10:20

Figure 10.31 shows an obje…

02:20

A compound disk of outside…

03:30

01:45

04:17

03:11

Measuring I. As an intern …

03:25

Measuring $I .$ As an inte…

03:20

A thin uniform bar has two…

05:37

03:23

A thin, flat, uniform disk…

05:52

Center of mass, moments of…

throughout this problem, I'm going to be referring to Table nine to since that table contains all the really commonly use moments of inertia and some part ay, we're looking at an object that is Iran. And then there's two essentially point masses On the end of it. The axis of rotation is this. And so it's rotating around in a circle like this. So I total is going to be equal tio home ownership of the bar or the cylinder, plus two times the moment of inertia of the masses. Since they're symmetrically distributed across the access here now going to table 19 we see that this is 1/3 times the mass of the war times l squared plus two and then I'm on this term. And then the moment ownership appoint mass is just the mass, which I'm going to live a little outing for each of these guys. So it's a little and this is M bar and then the radius from the axis out to the point object, which in this case, is El Bar. Actually, I'm just calling that l for now. So obviously was l. So in this case, that is all and So it's L over two square and then plugging in the values that give us a problem. We can easily find this to be 1.8 kilograms meter square in part B. R. Access is now long one of the masses. And so we have a situation like this this mass here street as a point mass. And since it's already on the axis, it doesn't contribute anything to the moment of inertia. So we're just calculated moment, Inertia of the Rod and then the point mess out here, this is again of like, del. This is going to denote by capitalism and this by a little. And so I total in this case is equal to 1/3 l squared. That's the contribution from the Rod. And I got it from table 92 and I'm adding the oil mill squared or this is for the point mass at a distance. L l now playing values into this expression gives 4.69 kilograms per meter squared. Finally, in Parsi we have hoop and then from the inside there are spokes and in their six in total. So it looks like this. So I total will be eye of the hoop, plus six times alone. Inertial spoke because they're symmetrically place around the access here. The access in this case is going into the page so that its rotating this way. And so I'm getting these from table nine to at this point, the moment her shove the hoop is the mass of the hoop, which I'm gonna label by Capital M. And then I'll label each of the spokes with mass a little, um, but the inertia of the hoop is the massive hoop times the radius squared. Where, um, we'll call this a capital R. And then I'm adding six times the inertia of the spokes, and each one has milliner shit. 1/3 massive spoke Time's ready, So spoke square. And then now plugging in the values into this expression gives 0.854 kilograms meter squared, and that's it

View More Answers From This Book

Find Another Textbook

In mathematics, a proof is a sequence of statements given to explain how a c…

In physics, rotational dynamics is the study of the kinematics and kinetics …

Calculate the moment of inertia of each of the following uniform objects abo…

A uniform disk of radius $R$ is cut in half so that the remaining half has m…

Perpendicular-Axis Theorem. Consider a rigid body that is a thin, plane shee…

The parallel axis theorem provides a useful way to calculate the moment of i…

The moments and product of inertia of an L4 $\times 3 \times \frac{1}{4}$ -i…

A solid circular disk has a mass of 1.2 kg and a radius of 0.16 m. Each of t…

Two metal disks, one with radius $R_1 =$ 2.50 cm and mass $M_1 =$ 0.80 kg an…

Figure 10.31 shows an object of mass $M$ with one axis through its center of…

A compound disk of outside diameter 140.0 cm is made up of a uniform solid d…

A compound disk of outside diameter 140.0 $\mathrm{cm}$ is made up of a unif…

Two metal disks, one with radius $R_{1}=2.50 \mathrm{cm}$ and mass $M_{1}=0.…

Measuring I. As an intern with an engineering firm, you are asked to measure…

Measuring $I .$ As an intern with an engineering firm, you are asked to meas…

A thin uniform bar has two small balls glued to its ends. The bar is 2.00 $\…

Calculate the moment of inertia of a thin plate, in the shape of a right tri…

A thin, flat, uniform disk has mass $M$ and radius $R .$ A circular hole of …

Center of mass, moments of inertia Find the center of mass,the moment of…

01:51

$\bullet$ Lung volume. The total lung volume for a typical person is 6.00 L.…

03:58

A certain type of propeller blade can be modeled as a thin uniform bar 2.50 …

03:26

football is thrown with an initial upward velocity component of 15.0 $\mathr…

02:46

.. Hiking the Appalachian Trail. The Appalachian Trail runs from Mt. Katahdi…

04:46

$\bullet$$\bullet$ At an altitude of $11,000 \mathrm{m}$ (a typical cruising…

02:17

Electric eels. Electric eels generate electric pulses along their skin that …

05:23

An ant is crawling along a straight wire, which we shall call the $x$ axis, …

03:42

An electric fan is turned off, and its angular velocity decreases uniformly …

02:29

$\bullet$ A uniform marble rolls down a symmetric bowl, starting from rest a…

02:59

$\bullet$ Friction at the hip joint. Fig-ure 5.51 shows the bone structu…