which-of-the-following-objects-has-the-greatest-rotational-inertia-a-a-1-mathrmkg-solid-ball-with-ra

Question

Which of the following objects has the greatest rotational inertia?
(A) A 1 $\mathrm{kg}$ solid ball with radius of 5 $\mathrm{cm}$
(B) A1 kg hollow ball with radius of 5 $\mathrm{cm}$
(C) A 5 $\mathrm{kg}$ solid ball with radius of 5 $\mathrm{cm}$
(D) A 5 $\mathrm{kg}$ hollow ball with radius 5 $\mathrm{cm}$

Salamat Ali · Accepted Answer

rotational inertia. It&#x27;s proportional to salutation. Inertia rise proportional to the muscle for an object and also proportional to the distance from a tradition of access. So Option Deke is the right answer because of the high marks and the greater distance from excess of tradition.

Sarah Mccrumb · Answer

everybody. So we want to rank the following objects. Order the circular velocity. So the V&#x27;s circular velocity equals the greater grab the gravity Constant times the mass of the earth divided by the radius of the earth. OK, so let&#x27;s do a and we do not have Teoh care about for this the small, the mass of the objects Because the earth is gonna be bigger, there&#x27;s going to be negotiable. Okay, so here for the grabby constant, we have 6.6 seven times 10 to the negative 11 m, three kilograms per second squared. Okay, The mass of the earth is gonna be 5.97 times 10 to negative 24 kilograms. Okay, this is a massive earth now for a So we&#x27;re doing a and it says its half of the radius. So it says are being earth halfway to the moon. And because of that, we have the moon&#x27;s radius here three times 10 to the eight meters to buy it by half class, the earth&#x27;s radius. So 6.38 times 10 to the eight. Okay. And if we do that, we&#x27;re gonna get 1416.6 meters per second. Okay, And now we&#x27;re gonna go on to be There we go. So be was given to us as object orbiting just above the earth&#x27;s surface. So here we have Besart, and I&#x27;m not going to rewrite the G and M because you can just look right here. So that&#x27;s the G m here. Okay, here the only have the earth&#x27;s radius because we&#x27;re just above the Earth&#x27;s and don&#x27;t have to worry about the moon&#x27;s radius for this one. Because of that, this is going to equal some 100 with 7900.23 meters per second. And I just realized my meters per second Looks like Meteors, per g. There we go, but and now we&#x27;re gonna go on to see so see the view, sir. Okay, we&#x27;re going to gm again because this is has not changed. And now the sea is gonna be 3.8 times Ted to the eighth meters. So the radius of the moon, plus the radius of the earth 6.384 zero times tend to eight. Okay. And so this has been equal 1115 meters per second. Okay, Now we&#x27;re gonna go down to D. De says object orbiting 1/4 of the way to the moon. 1/4 means it&#x27;s 14 Okay, we have G M. Now we have 6.38 radius of the earth climbs 10 to 8 plus 0.95 times 10 to 8. Okay. And that&#x27;s the quarter amount of the moon. So we have this for the moon, but by four. OK, now that we get here, guys, So that&#x27;s gonna be 1900 e 1.86 meters per second. So now we gotta length, um And I&#x27;m just gonna rewrite these out for you. So that way you know what is right just cause so that way Don&#x27;t score. Welcome to show. Okay, be waas 7900.23 meters per second. See Waas 1000 team meters per second and d wise 1981. Appoint 86 meters per second and it asks us to break the family objects in order for the Boston from the smallest to the largest. Okay, so from this, we can see that c is gonna be the smallest. Okay, and was gonna be greater than that is it Looks like a is next. Then D then be okay. And that is your guys his answer. Thank you.

Ze-Han Lee · Answer

So in this problem, we have two balls. They have the same size and they have this in mess. So, uh, and also, if we are, if we accepted the same same amount of torque on them, so want to see which one rotate faster The relation between a torque ended. Ah, and the rotation speed, it&#x27;s ah torque equal. I times omega. So the call here means the pork in the eyes, the moment in nature and only guys angle velocity. So, uh, as you can see that that we have the same torque on both balls, right? So if the woman the inertial larger, then the speaker is lower, so we just need to look at the moment Inertia of the two bowls. So for the first polls Ah, the masses evenly distributed inside. Okay. And for a 2nd 1 that mass only only distributed on the on the surface, off the off the ball. Okay, It&#x27;s only on the surface, so we know that to the definition of the moment. Nurture is ah, I equal square root. Ah, so are square times D. M. Ray. So basically like ah, if so forth, so fuck somebody will look at this fear for this point. Ah, supposed masses tm then we used ah is that these things are Then we used our square times tm tripped in the moment inertia at this point and with some all of them together to obtain the total moment Inertial this fear okay. And ah for the solid for the solid solid ball case will see that we also have some We have some messes inside, right, for the mess is inside the radius are is actually smaller. So in that sense we see that a clearly no moment inertial This one I saw it is actually smaller. Then the woman and there Sure that is solid. Well, when the nurture then this Ah, I ah, my sphere! Okay, so you say that Ah, because the moment never showed this one smaller So the ah ah, English speed off. This one is larger. So in essence, we see that the omega solid It&#x27;s not Jer, don&#x27;t make us fear. Okay? So because they have the same size or they have the same radius, right? So the velocity v off the solid is larger than the velocity of the sphere. Okay,

Abhishek Jana · Answer

So in this problem, the only thing that will change here is the moment of inertia. But other than that, all the calculations will be same. So first of all, we should identify the total kinetic energy, which is KCM plus keon rotation. Where&#x27;s Casey? Um, is Ah, let&#x27;s ah, if the object is just, ah, uniforms, solid cylinder. So let&#x27;s say this is the cylinder that we have. And if if this senator&#x27;s rolling without sleeping, that means the center of Mass is moving linearly great. And because of that, we have, ah, velocity associated with it. And that&#x27;s why we have, ah, kinetic energy, which is associated with the center of Mass. And then we have a rotational, kinetic energy, since the cylinder is rolling without slipping. So and also for an object that is rolling without sleeping when we set a definition that the velocity of the central mass is equal to our times omega. So this is just when we have a condition off rolling without slipping. So now if we want to write the faction off total candidate energy, that is rotational, uh, so that means the fraction let&#x27;s eh, it&#x27;s right that as fraction will be equal toe the rotational part of the control candidate energy, which is 1/2 the moment of inertia when the accesses dissenter. Yeah, that&#x27;s the access. Sorry for my poor drawing. Um, then we have omega squared, and we divide that by the total kind of energy, which is, um, half off em VC and squared. Since we say that this is just a linear motion. So we have the linear candidate energy plus the rotation part, which is I&#x27;ve, uh I see em omega squared. All right, so we&#x27;ll be using this equation on ly for different parts on as you mentioned, that on Lee Thing will change is the moment of inertia. So let&#x27;s see for ah, for the uniforms solid cylinder. We know that I cm or the moment of inertia of the serum A of this lender is half off and r squared. And if we use this will see that the ratio, or diffraction, will be 1/3. Similarly for the uniform&#x27;s speared uniforms. Fear will have I see em as two over five in my r squared, so the ratio will be to over seven for the thin World Hollow sphere. IBM is to over three m r squared, and that gives us a ratio off to over five. And finally, for the hollow cylinder with our radios are in a radius are by two Our eyes See em is five by eight m r squared. So their issue becomes five by 13. Thank you.

Shoukat Ali · Answer

in this problem, we are asked to calculate the fraction off the rotational Canada energy in total Canada. Energy for the Given Objects, which is Colonel Tasted he wanted by K was concluded in general by writing the total energy years cables to translational plus irritation writing values. For this K translation and adaptation. We will get PayPal&#x27;s to one by two and we squared plus one by do Iomega Square. No rotation divided by K equals to one by two Iomega Square You worried by one by two m we square plus one by two Iomega Square The squaring can be simplify It is irritation you wanted by cables to one you wanted by and we&#x27;re squared divided by I plus one So call it equation No, for uniforms sorts selling there I calls to one by to him or square Now sitting the well off this Ianto equation a We will get irritation wanted by cake was 21 divided by one by two plus one equals two one by three. Now fire uniforms fair Michael&#x27;s to to buy five more square now setting this well you into equation again We will get irritation by K equals to one by five by two plus one People&#x27;s too two by seven Now Tin World always fair. Eichel&#x27;s to two by three m R square Now setting this world even into equation air. We will get you&#x27;re a patient by cables to one by three by two plus one equals two, two by five No, for hollow cylinder Michael&#x27;s to five by it Amar Square. Now again, setting this well, you&#x27;re fighting to equation There we will get irritation you wanted by cables to one by and my five plus one equals two flyboy 30 so in awe of the question

Joseph Petrullo · Answer

So for this question, we can think about angular. Momentum is equal to our cross P, where P is often defined as just its mass times its velocity. And so the angular momentum of an object is going to depend on the objects mass, the objects rotation, speed and clearly because of the are the objects radius. And so therefore, the answer is D all of the above.

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In one semester, Doug and Laura spent a combined …

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