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Four small 0.200 $\mathrm{kg}$ spheres, each of which you can regardas a point mass, are arranged in a square 0.400 $\mathrm{m}$ on a side andconnected by light rods. (See Figure $9.26 . )$ Find the moment of inertia of the system about an axis (a) through the center of the square, perpendicular to its plane at point $O ;$ (b) along the line$A B ;$ and $(c)$ along the line $C D .$

a) 0.064 $\mathrm{kg} \cdot \mathrm{m}^{2}$b) 0.032 $\mathrm{kg} \cdot \mathrm{m}^{2}$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Sheffield

McMaster University

Lectures

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In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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in the first part of discussion, we're going to get let the moment off Inertia of the human system. A boat, a point. Oh, which is perpendicular to the plan. So let the moment off, inertia about this point, ese, I not in the first part of this question we are going to kill led the moment off Inertia off the given system about a nexus which is perpendicular to the plan and a passing through the point. Oh, let this moment off in ashes. I know in order to guilt Let this moment off Inertia. We need to find the moment on which is represented by D. What l is The lentil decides off the square, then using the Patagonia serum we can, right? Deepa ls two squared off. Ellie would buy to hold square plus rewarded by duel square so it can be simplify. It is d equals two lt wanted by squared off too. No looks right at the moment of Phoenicia for the system I not equal stupid for him in tow, divided by a squared off to hold square. So quality quite in one. Now sitting the Williams into this equation even get I know articles to foreign to 0.200 k g into little 0.400 You want to buy a squared off two meter hole square, so this with us I know tickles, too. 0.0 64 Cajun meter square. So this is the answer. First part of this question. Let's come toward the second part of this question in this part of the question we are going to kill. Fled the moment off. Inertia off the system along the line. Abby, that's called this moment off. Inertia I A B No, let's ride the formula for a baby, which is I A B equals two for him, held by two whole square so called a Dick Whiting to now sitting the Williams into this equation, we will get I A B equals two 14 to 0.0 k g into 0.400 meter divided by two old square. So this will view us I A B people's too 0.0 three to kadji meter square. So this is the answer off. Second part of this question. Now let's come toward the last part of this question in this part of the question We are going to kill. Let the moment off inertia off the system along the line CD. So call the moment of inertia. I see d Let's write that formula for I c d I see the equals toe to enter into l d wanted by squared off to all square So call it quite in three. Now setting the world is into this question we would get I see the equals to two into 0.200 Casey into 0.400 meter You wanted by a squared off to old square. So this with us I see the equals two 0.32 cagey meter square. So this is the answer the third part of this question so thank you.

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