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Review Constarbicycle wheel has an initial angular velocity of 30 radIf its angular acceleration constant and equal 0 200 rad/s? what is its angular velocity att = ...

Question

Review Constarbicycle wheel has an initial angular velocity of 30 radIf its angular acceleration constant and equal 0 200 rad/s? what is its angular velocity att = 2.50 5? (Assume the acceleration and velocity have the same direction)Fxpress your answer in radiang per secondAEdradSubmitRequest AnswerPar BThrough what angle has the wheel turned between Expross Vour answvor radiansand2.50 $?Azq4e =rad

Review Constar bicycle wheel has an initial angular velocity of 30 rad If its angular acceleration constant and equal 0 200 rad/s? what is its angular velocity att = 2.50 5? (Assume the acceleration and velocity have the same direction) Fxpress your answer in radiang per second AEd rad Submit Request Answer Par B Through what angle has the wheel turned between Expross Vour answvor radians and 2.50 $? Azq 4e = rad



Answers

A bicycle wheel has an initial angular velocity of 1.50 $\mathrm{rad} / \mathrm{s}$ .
(a) If its angular acceleration is constant and equal to 0.300 $\mathrm{rad} / \mathrm{s}^{2}$ ,
what is its angular velocity at $t=2.50 \mathrm{s} ?$ (b) Through what angle
has the wheel turned between $t=0$ and $t=2.50 \mathrm{s} ?$

For this problem. We're given the initial angler velocity of school. Um, it's, ah, constant acceleration and were asked to find its angular velocity that to you close 2.5 seconds. And also the angle that the will has turned between, um, zero second and 2.5 seconds. Okay, So for part A, we just uses your general expression from i t, which is sequel to the initial value off. The England will see one point 5,000,000 per second class. The constant acceleration 7.2 Really in per second squared. Replied about time t down. Wait. We're simply plugging t equals 2.5 seconds here to find that, um, angular velocity ese to reading per second part B of the problem where required, Find Delta Zeta. So vs, um, equal to the any role off omega T J T from zero second to 2.5 seconds. The integrated amenity has the above expression. So, um, after integration was simply got 1.5 two plus 1/2 I'm sure a point too. Times two squared, huh? Was the upper limit to 15 in Lorna Majerle. Seconds. So, a plugging numbers, we get, uh, the change to the n gold rotational angle to be 4.3 75 Really,

So here we only at we have givens on a wheel. We have the radius of the wheel point two meters and then we have the a linear velocity of the wheel. So fifty meters per second at T equals three seconds. And then we had the tangential acceleration of negative ten point zero meters per second squared. At this point, we can find our angular acceleration for a This is going to be equal to a ten over our or negative ten point zero over point two. And that's going to be negative fifty radiance per second squared. At this point, we can also find the angular velocity AT T equals three seconds. So there's going to be able to the linear velocity divided by our. So it'LL be fifty divided by point two and that's going to be equal to two hundred and fifty radiance per second. I apologize. Two, two hundred and fifty ratings per second. And then to find the final velocity, we simply need Teo. Take this. We have to take this and say omega f equals Omega initial plus Alfa t and then we can solve for Omega initial. So Megan initial will equal Omega F minus Alpha T. So this is we're trying to solve for tea. The angular velocity at T equals zero seconds. So at this point, we can say Okay, off initial equals two fifty what we just found and then minus the angular acceleration of negative fifty times, three seconds. So this will be four hundred radiance per second. So this will be the initial angular velocity and that first, see, they're asking us for the final angular displacement. So Omega F equals Sorry. Fate lf Eagle State initial plus omega initial T plus half Alfa t squared and there's going to be equal to zero because we're starting from zero. So this will be weakened. Just ah, substitute directly and say four hundred and we're doing the full two seconds. Sorry. Two full three seconds. My apologies. Um and plus half of negative fifty three squared again. Three my parties. So this is going to equal nine hundred and seventy five Iranians, and this will be equal to your final angular displacement for D. Um, they're asking us for the final angular, um rather the angular Rather the angular velocity needed such that the radial acceleration is equal to G. So a sweet city a radio equals these squared over r which equals our omega squared, which has two equal G. So that means that Omega is going equal, radical g over our and we can just say nine point eight, divided by point two, Diskant equal seven point zero radiance per second. So this is the Omega needed, such that, eh? Union equals J. So that would be your answer for De. And that's the end of the solution. Thank you for watching.

So we're told that a real accelerates at five radiance per second squared and it travels through 300 radiance. And so we're trying to find what the final angular velocity is after its travel, this 300 radiance and also how long it took to travel through those 300 readings. So the easiest way to do this is to use our Kinnah Matic formulas to I'm so for what we're looking for. So for part A, we're trying to find the final angular velocity, and so we can use this top equation here to solve for W f. So this equation states that the final angular velocity squared is equal to the initial angular velocity squared plus two times the angular acceleration times the, um, distance traveled in radiance. So when we write this out, we're going to have omega f squared is equal to. So the initial angular velocity is told to us it's just zero. Um, so we can get rid of that two times the angular acceleration, which is five times the, um, rotational positions, or how how far it's traveled, which is through ended radiance. And then we'll see that the final angular um velocity is equal to the square root of 3000. And so when we, um, take the square root of 3000 we get the final angular velocity is equal to 54 0.77 radiance for a second. All right, so now that we have this, we can figure out how long it took for it to go through this. 300 readings per second using this second formula, which states that the final, um, the final angular velocity is equal to the initial angular velocity, plus the angular acceleration times the time, and so the let's write this out. So the final angular velocity is equal to the initial angular velocity, which is zero times the angular excel are plus, plus the angular acceleration times time. Certain angular acceleration is five times that time, which we're trying to figure out. And so the time it takes to go 300 radiance is equal to 500 are sorry, 54.77 divided by five, which is equal to 10.95 seconds. So these are your two answers for this problem?

Everybody. So for this one, um, we need to find Calculate the wheels. Constant acceleration. Okay, so we have a similar solutions. A are uber are and me at negative 10 meters per second squared, divided by 0.2 meters. This you do negative 50 radiance for the second square. Now for B, it's asking us Teoh, calculate the England blast ease at 30 So of this we have finger blast e the r equals 50 divide by 0.2 leaders. Okay. And from this whole thing, you have meters for seconds. Variously now was the need to 50 radiance for seconds with this And then for the second line me how velocity in los initial plus So reaching times t an enemy have to 50 Radiance for seconds equals the initial minus 50 radiance per second squared times three let's few seconds and your initial is going to be 400. Regan's second now or see he's asking, um, since asking us through the angle the wheel. And so here we have angle in this old times t plus one Hillary where? So what's him again? You know Indians Second times three seconds plus 1/2 times native Indians, where Heinz Three seconds squared. And this whole thing is gonna give Arsene Hunger on 75. Okay. And now for D. He is asking us at what time of the radio celebration people, okay. And so we have this year old are weird. And then we need to find our with video or in the way and seven lead. Ian's seconds. Nobody anglers relation meets England philosophy from missile velocity region T and pulls the Ingwer Waske minus Englander Initial that is a celebration pulls seven radius second minus 400 Reuse with second divided by negative 54 seconds. Where and from this you get Southern 0.6, you guys.


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