5

Two disks spin opposite directions shown; Without exerting any external torques_ the two objects collide together so that afterwards they spin as single object;6.00...

Question

Two disks spin opposite directions shown; Without exerting any external torques_ the two objects collide together so that afterwards they spin as single object;6.00 200 emrevfsMz = 8.O0 kg Rz = 250cm 14.0 rev/sHow fast (in rev/s) will the objects be spinning after they stick together?

Two disks spin opposite directions shown; Without exerting any external torques_ the two objects collide together so that afterwards they spin as single object; 6.00 200 em revfs Mz = 8.O0 kg Rz = 250cm 14.0 rev/s How fast (in rev/s) will the objects be spinning after they stick together?



Answers

Two disks each have a mass of $5 \mathrm{kg}$ and a radius $300 \mathrm{mm}$. They spin as shown at the rate of $\omega_{1}=1200 \mathrm{rpm}$ about a rod $A B$ of negligible mass that rotates about the horizontal $z$ axis at the rate of $\omega_{2}=60 \mathrm{rpm}$. (a) Determine the dynamic reactions at points $C$ and $D .$ (b) Solve part (a) assuming that the direction of spin of disk $A$ is reversed.

In the execution given data is That is two discs are mounted Yeah on low friction bearing on the same excel and can be brought together. So did the couple and rooted as one unit. Now in the community thing that the first days rotational inertia is given. That is again stated Ivan About that actual value is that is 3.30 kg meters squared. And this first disc is said is spinning counterclockwise. So the action is also given that this counterclockwise With angular speed is Cuban. That is Omega one for first disk. That is 4 50 revolution for a minute. Yeah. No in the kitchen whether it is saying that the second is Having rotational inertia is given that is I two value will be, that is about its center center taxes. Central axis value is 6.60 kg meters square. And this second this is set spinning counterclockwise and Anglo Swedish human. That is Omega II is equal to 900 revolution permanent. So that means the direction for both. This is same, that is counter clockwise so no further in the kitchen. It is saying that after the couple together than we have to solve the given kitchen. And in this vision there are two parts given. So Sorry three parts is given. So I will solo All the parts one x 1. So let's start asking the future in the party. It is asking that after the couple together we have to find the angler is speed. So Mhm. For finding this angular speed or party. Yeah, I will be playing a angular momentum conservation. So according to this angular momentum conservation, the law will be written as there is Ivan omega one plus I to omega two is equal to I one plus I to times of omega. So here I want Omega one is a angular speed of Yes, first this sorry, angular momentum of first disk and I to omega two is a angular momentum of second disk and I one plus I to times of omega is a angular momentum of system after the couple together. So you're after simplifying we have two main target is we have to find the value of this omega. That means angular is good of the days after the couple together so no simplified Then I will get the equation for omega that is equal to I one plus I to. Sorry I Want Omega one. Yes I do Omega two divided by one plus I do. So now you said that uh that is given value. I won omega one and I two omega two. That it's human. So here I'm shooting this data so that I will get the answer for party. So where you will be after simplifying value will be that is 750 rpm. And one thing also remember that era. I had also included the sign that is you can see that the both days having same direction that is counter clockwise. That means I considered omega will be written as that is having posed to sign so that after it I will simplify it using this law of conservation of angular momentum so that I will get the final value of part A answer for apartheid. That is omega will be after the couple I considered where you angles will will be that is 750 rpm. Now come to the next part that is be So in the part B. It is asking it it is Instead the second disk is set it spinning clockwise at 900 rpm, then what are their angular speed And in the party this has hinted the direction of rotation after the couple together. So yeah, for getting the answer, part B of part B. The condition that is here decision is going to change for second days. That is new direction will be given that is clockwise direction for second is and omega two is human same value, that is 900 revolutions per minute. So now for getting the answer for part we get miss omega after the coupling again I will use the angular momentum conservation so it will be a witness. That is Ivan omega one minus I. To omega two divided by one plus I to times of omega. Here you can see that I also included the sign and for first time I had taken the party sign. And for second term on the left side I had taken the negative sign because you can see that the second term is saying that the angular momentum of second disk and the decision is given that is clockwise. So that means I can say that the omega value how that is negative value. So did after multiplying did you negative sign for a second term? So no, likely put the magnitude of the value of given data and simplify it. Then I will get the answer for omega that if I can see that before simplifying fight to make a question by using this a bow line so I can set it. Omega will be equal to I one. Omega one minus I to omega two divided by I one plus I to now some of the data, so I will get omega that is equal to 3.3 multiplied by 4 50 6.6. multiplied by 900. Yeah, divided by 3.3 plus 6.6. So value will be, that is out of selling value is there is minus 450 revolution per minute. So magnitude of angles here will be that is in the question, it is only asking magnitude, so after the couple. So valuable, that is 4 50 revolutions per minute. And in the party it is asking the direction of this omega which is I have sold in the part B. So for parts, the answer will be, that is, I can say that there is a you can see that in the part of the answer is having negative sign. So that means it is a sign that the omega is clockwise direction, that is In the direction of 2nd, this initial angular velocity. So my answer is for party that is clockwise direction. So I had sold the occasion completely by giving the old answer. But so for part of the answer is that is I can say that 750 rpm and for part B answer is that is 450 rpm, and for part of the answer is that it's clockwise direction. Thank you.

In this problem on the topic of angular momentum, we have two discs that are mounted on bearings on the same axle and can be brought together so that the couple and rotate as a unit, the first disc has rotational inertia 3.3 kg meter squared about its central axis And spins counterclockwise at 450 rounds per minute. The second disc has rotational inertia is 6.6 kg meters squared about its central axis And it's spinning counterclockwise at 900 rpm, a couple together and we want to know their angular speed after coupling. And if we are told that the second disk, is it, is that spinning clockwise at 900 rounds per minute? We want to find the angular speed and direction of rotation after the couple. Now we'll apply the conservation of momentum of angular momentum for both disks. And we get I one omega one, That's the that for disk to I two or make it too is equal to I won plus I to tempt the final angular speed omega. So the speed after coupling. Therefore, by rearranging this equation, omega is equal to I won Omega one plus I too. Omega two divided by I one it plus I too, Putting in our values, we get this to be 3.3 kg. Me too squid, times 450 revolutions per minute plus 6.6 Kg meter squared times 900 revolutions per minute, divided by the sum of the rotational initials, 3.3 kg meters squared plus 6.6 kg meter squared, which gives the angler speed after coupling To be 750 revolutions per minute and for part B. In this case we obtained omega to be I won omega one plus I two, Omega 2, divided by I one plus I to as before. However, when we put the values in, we get this to be 3.3 Kg meters squared times 450 RR per minute plus the rotational inertia for the second disk, 6.6 kg meter squared. Now multiplied by the angular speed of this too is now minus 900 rpm as it is now moving in the opposite direction. And all of this divided by I one plus I to This is 3.3 kg meters squared plus 6.6 k g meter squared. This gives the final angular speed to the minus 400 and 50 revolutions permit it, or A magnitude of 450 revolutions per minute and and now for part C. Okay, we can see that the minus sign indicates that omega is clockwise. That is in the direction of the 2nd disks, initial angular velocity

Now we have two discs moderate on a low friction bearings here and the so they're on the same axle and they bring we brought together so that the couple the the the couple and rotate as one unit. So basically somehow we can, you know, make attach these to one another so they rotate together. Now the first disc we're told has a rotational inertia and in angular velocity. And the second disk has a different rotational inertia and a different angular velocity. No that's that. You know this is the second disk has twice the angular inertia and twice the angular velocity. Now we want to were asked to figure out what the um we have to figure out what the um Angela velocity is of the system after. So this is initially before they're obviously they're not coupled together and so we couple them together and going to figure out what the final result in angular velocity is of this of when they're attached to one another. So the initial angle of velocity. Um I don't know why I have a one in there, but oops all right, so we have the initial and we can figure out that is J one times omega one plus J two times omega too. And obviously you can get the angle of velocity in terms of radiance per second, in terms of by unit conversion. But it turns out we won't need to do that actually. And then afterwards, because they're rotating together the angler, the rotational momentum rotational inertia is just J one plus J two and they have the same angular velocity. So we can use this expression here and we can solve for omega prime. We get here and now again, because there's just going from omega two F. There's just a factor of, you know, 60/2 pi or to pi over 60. Um and each one of these terms that would all canceled. So you can write this expression here in terms of um f and you know, using it in rpm. So we um we plug everything in here in terms of the units of rpm And we get the and in the end it's going um 750 rpm. Which makes sense because again it's going, it's gonna it should we expect it to be somewhere in between here and here. Um And we should expect that it should be kind of closer to this value here because the rotational inertia is much higher of this disk here and that is indeed the case. Um Now we're as we're told that now this is the second disk here is spending the opposite direction. So we have, you know, F2 is now -100 -900 rpm. So we can get the same formula applies. So plugging in -900 rpm here we get -70 rpm as our um as our angular velocity. And that's um in the opposite direction. Obviously. So and again we shouldn't be surprised because um you know, the the angular momentum of this guy is much greater than this guy, so when we couple of them, if they're spinning in opposite directions and we all of sudden lock them together, we would expect them to be spinning in the direction of the disk that had the most, the greater angular momentum to begin with. So we get -70 rpm in the in the clockwise direction. They were.

Okay, so in the first part of this problem, the two discs are spending in the same direction, disk, number one has a rotational inertia 3.3 kg meter square And a rotational speed of 450 rpm. This number two has a rotational inertia of 6.6 kg metre squared. And they rotational speed of 900 revolutions per minute. We want to know what their new speed is after they couple together. So for this we can use uh conservation of angular momentum where the total angular momentum before the couple has to equal the total of angular momentum. After the um And before the couple there they have individual and angular momentum's so um it's gonna be I won omega one plus I two, Omega 2 and that's going to equal the combined rotational inertia Times Omega three or the final Omega. So, Omega three is going to equal this whole thing over here, divided by the combined rotational inertia except and that is going to give us a value of 700 and 50 revolutions per minute. Yeah, all right. Uh And then in part B we are told that we are going to spend the second disk in the opposite direction. So now, instead of spinning it in the same direction as the first disc, we're going to spin it in the opposite direction. Um So the same thing holds true except at the beginning here, we're gonna actually subtract um These two values. Um So the we're going to have uh set up the same Thing I Omega one minus to make it to, and so we're going to get a negative here because they're just in the opposite direction. So um and then that's going to equal the combined mass same as before or the combined rotational inertia Same as before Times Omega three. And so mega hurry is I want to make a 1 -1 to make too over the combined to show the nurses. And if we plug in our values for that, We get negative 450 revolutions per minute. Or in other words, 450 revolutions in the opposite direction of the first case. So 450 revolutions per minute in the same direction as the second disk.


Similar Solved Questions

5 answers
Describe each step in in the process yOu would use to prepare 1.5 L of 0.35 M sodium acetate (NaOAc); at pH 5.5, from sodium acetate trihydrate (fw 135.08 g/mol) You will find that when YOu dissolve this salt in our double-distilled water; the pH of the solution is about 8.0 ~ &.2. Be sure t0 explain how you will adjust the pH t0 5.5 using HCI or NaOH (not acetic acid, which would alter the molar concentration of acetate ion).
Describe each step in in the process yOu would use to prepare 1.5 L of 0.35 M sodium acetate (NaOAc); at pH 5.5, from sodium acetate trihydrate (fw 135.08 g/mol) You will find that when YOu dissolve this salt in our double-distilled water; the pH of the solution is about 8.0 ~ &.2. Be sure t0 ex...
5 answers
Find the distance from the point (1,2,3) to the line € = 2+t,y =3, : = 1-3t
Find the distance from the point (1,2,3) to the line € = 2+t,y =3, : = 1-3t...
5 answers
17. The equilibrium that exists between the keto and enol forms of aldehydes ad ketones is known aS: stereoisomerism configurational isomerism C) geometric isomerism D) tautomerism E) positional isomerism
17. The equilibrium that exists between the keto and enol forms of aldehydes ad ketones is known aS: stereoisomerism configurational isomerism C) geometric isomerism D) tautomerism E) positional isomerism...
5 answers
4. The graph off(x) = is reflected about the Y-axis and compressed vertically by a factor of 5 5 What is the equation ofthe new function, g(x)? State its Y-intercept; domain, and range 6. The graph off(x) = (1.68)* is shifted right 3 units, stretched vertically by a factor of 2, reflected about the x-axis, and then shifted downward 3 units What is the equation of the new function, g(x)? State its y-intercept (to the nearest thousandth), domain, and range.
4. The graph off(x) = is reflected about the Y-axis and compressed vertically by a factor of 5 5 What is the equation ofthe new function, g(x)? State its Y-intercept; domain, and range 6. The graph off(x) = (1.68)* is shifted right 3 units, stretched vertically by a factor of 2, reflected about the...
4 answers
The distance between Earth and the Moon Is reduced to one third its original distance: The gravitational force between them becomestimcs |rgct(Imics smnalce(imes smallcrtnes |arger
The distance between Earth and the Moon Is reduced to one third its original distance: The gravitational force between them becomes timcs |rgct (Imics smnalce (imes smallcr tnes |arger...
5 answers
Question 4 (1 point)Aspirin has a formula CoH8O4: The molar mass of aspirin is1) 180 g2) 325 &3) 220 g4) 95 g:
Question 4 (1 point) Aspirin has a formula CoH8O4: The molar mass of aspirin is 1) 180 g 2) 325 & 3) 220 g 4) 95 g:...
1 answers
Write the first five terms of the sequence. $$a_{n}=\sin \frac{n \pi}{2}$$
Write the first five terms of the sequence. $$a_{n}=\sin \frac{n \pi}{2}$$...
5 answers
Find $m$ for each $m$ -ary tree.
Find $m$ for each $m$ -ary tree....
5 answers
2) Which of the following would NOT be a physical change? freezing water t0 make ice cubes melting gold t t0 make jewelry burning gasoline in lawnmower boiling water for soup3) Which ofthe following NOT physical change? grating cheese melting cheese fermenting of cheese IIXIn LWo cheeses in bow /dedPrTSC SYSRd09
2) Which of the following would NOT be a physical change? freezing water t0 make ice cubes melting gold t t0 make jewelry burning gasoline in lawnmower boiling water for soup 3) Which ofthe following NOT physical change? grating cheese melting cheese fermenting of cheese IIXIn LWo cheeses in bow / d...
5 answers
1 a) Starting with supplied voltage of 85V, create a circuit ofresistors and one lightbulb where the lightbulb has 15V across itand 1A going through it.b) Starting with a lightbulb with a resistance of 5 Ω, create acircuit where the lightbulb has 10V across it and battery isproducing 5A total.
1 a) Starting with supplied voltage of 85V, create a circuit of resistors and one lightbulb where the lightbulb has 15V across it and 1A going through it. b) Starting with a lightbulb with a resistance of 5 Ω, create a circuit where the lightbulb has 10V across it and battery is producing 5A tota...
5 answers
Houestionie#Test Ithelsares Below fom convengence 4sing the Ratio Test In? Wg"HThe Limieefthe ratio test siniplifiesito Himg f(n) hwheref(n)]UThe Limnit i3: Kencer po forlinfinit MeedediBased on this the geres eeiec ainiamameUSuurna t CWeRHiwm
Houestionie #Test Ithelsares Below fom convengence 4sing the Ratio Test In? Wg" HThe Limieefthe ratio test siniplifiesito Himg f(n) hwhere f(n)] UThe Limnit i3: Kencer po forlinfinit Meededi Based on this the geres eeiec ainiamame USuurna t CWeRHiwm...
5 answers
A. Show the anomeric carbon: (1 pts) Draw B-D-Fructopyranose (2 pts)CHzohHO OHHOOHa-D-Fructopyranose (M) disaccharide (D) or Polysaccharide (P) (3 pts) Identify monosaccharide ChitinMannoseLactoseRibuloseRiboseMaltose7)If Disaccharide water: Monosaccharide Monosaccharide (Hydrolysis reaction) & Monosaccharide Disaccharide water (Dehydration synthesis) Monosaccharide What is the result of following reaction? points)Glucose ClucoseLactose water
A. Show the anomeric carbon: (1 pts) Draw B-D-Fructopyranose (2 pts) CHzoh HO OH HO OH a-D-Fructopyranose (M) disaccharide (D) or Polysaccharide (P) (3 pts) Identify monosaccharide Chitin Mannose Lactose Ribulose Ribose Maltose 7)If Disaccharide water: Monosaccharide Monosaccharide (Hydrolysis react...
5 answers
Fndi Xz (the probability distribution the system after two observatlons)the distribution vector Xo and the transition matrix0.25 0.600.15
Fndi Xz (the probability distribution the system after two observatlons) the distribution vector Xo and the transition matrix 0.25 0.60 0.15...
5 answers
Engulfed Photorynthetic bacterium FlastdJandandand /nnd 7SubmitAoqurat AnsworProvide Feodbackuar Rant A
Engulfed Photorynthetic bacterium Flastd Jand and and / nnd 7 Submit Aoqurat Answor Provide Feodback uar Rant A...
5 answers
Coorainarecectonqulai coorcinate systemThe polar coordinates of the same Dointare25.08). What are the values
coorainarec ectonqulai coorcinate system The polar coordinates of the same Dointare 25.08). What are the values...

-- 0.019774--