a-mechanical-wheel-initially-at-rest-on-the-floor-begins-rolling-forward-with-an-angular-acceleratio

Question

A mechanical wheel initially at rest on the floor begins rolling forward with an angular acceleration of 2$\pi \mathrm{rad} / \mathrm{s}^{2} .$ If the wheel has a radius of $2 \mathrm{m},$ what distance does the wheel travel in 3 seconds?
(A) 4$\pi \mathrm{m}$
(B) 6$\pi \mathrm{m}$
(C) 16$\pi \mathrm{m}$
(D) 18$\pi \mathrm{m}$

Vishal Gupta · Accepted Answer

Hi the given problem angular acceleration in mechanical wheel he has given us and fuck Is equal to two. Bye, radiant per second. The square. Its initial angular velocity is zero as the hell was addressed. Initially radius of the wheel. He&#x27;s given us our Is equal to two m. And we have to find the distance Travel by the wheel in a time duration of three second. So, first of all, we will find the angular displacement need by the wheel in three seconds, for which we will use second equation of rotational motion according to which the angular displacement will be given by data is equal to omega, not T las off alpha. D. Square. This is zero in the first time plus half alpha, Where alpha is two pi into the square of three seconds, cancelling this. To hear this angular displacement made by the will comes out to be 95 radiant. No, we know that the angular displacement covered. Sorry, The linear displacement covered by a circular hill in a complete rotation. If it is allowed to revolve over the ground in a complete rotation, the angular displacement will be equal to Dubai and the linear displacement will be equal to its circumference. Hence we can say distance linear distance cover by the wheel on to buy. Angular displacement is equal to circumference, which has given us to buy into art. And here are means radius is two m, so this is for white, so for angular displacement half of one. This linear displacement will be for bye bye. Two pi means this is two m. Hence for angular displacement of nine pi, this linear displacement will be two m, multiplied by nine pi means this is 18 by meter. The linear distance covered by the wheel over the ground. Hence, here we can say our option D. Is correct. Thank you.

Kristela Garcia · Answer

So in this problem were given an angular acceleration of two pi radiance for second square, a time interval of three seconds and a radius of two meters and were asked to determine the distance traveled. So we&#x27;re going to start off by applying a rotational kin o Matic equation. And our initial angular velocity was zero. So Seda is the number of rotations that we made in degrees. I&#x27;m sorry in radiance, and we can go ahead, plug in our values. For this, you have the 1/2 in the to counsel to get a angular displacement of nine pie. And so, if we divide nine Pai bi to pie, it tells us how many rotations we made. And again, I&#x27;m gonna leave this something to get 4.5 rotations. So our circumference is two pi r. And so four times are circumference is going to tell us our total distance traveled around so we can say to pi times radius too. So this is 4.5. Yeah. Gives us a total distance. Traveled of 18

Salamat Ali · Answer

the linear velocity or for real, this region Daisy is a call to a radius Time made out. We&#x27;re where we need Ah, Mega R is given So the Omega is a call to initial maker. We&#x27;re gonna plus acceleration times t so many naughty zero within polar exploration we have ease into radiance. Toured in for a second square time is after five seconds. So this gives us on May go Which is it, then? 10 radiance for a second. So we&#x27;ll substrate this value where we have radius is little 0.5 meter offer well danced in radiance per second. This gives us the meaning of a lost year for five meters per second off the wheel. So option C is the right answer.

Zhuxi Luo · Answer

for this problem, We&#x27;re given the diameter off the off the will to be 40 centimeters, which means it&#x27;s radius is 20 centimeters, or equivalently 0.2 meters were also given that the will starts from rest and accelerates with the constant angular acceleration three radian per second squared and we&#x27;re required to find ah, radio acceleration about the will after it has gone through its second revolution. Which means the angle it has, um, past is 4.2 times two. Yeah, Um, the problem asks us to find the radio acceleration using a equals omega squared. Times are in the first part of the problem. So we need the expression for omega. And this omega is related to the exploration by Omega course integration over acceleration. With respect to time, this gives us all the teeth. And to get two, we were used The following expression for theater. Hey, the is, um, integration of omega over tea. Plugging omega equals Salvati. This gives us 1/2 off a T squared and also we have city was full pie. So from this a question we consult for the time t to be skirt of eight pi over Alfa playing like the number for ALPA would get t equals 2.89 seconds. And now we can use, uh oh. Value calls. Omega equals Salvati, Omega squared, times up blooding L Because straight equals 2.89 and articles you want to. We got the radio exploration to be 15.1 meter per second squared. Right? Um, part B wants us to use an alternative expression for a a equals B squared over r. Recall that this, um, leaner velocity is equal to the Omega by V course Omega. So expression for a is to fully and this simply well reduces, too. Omega squared. Time&#x27;s up. So we were observed. This is exactly the same ecstatic expression. So obviously we&#x27;ll get the same number 13.1, meeting her second score.

Averell Hause · Answer

we can use Equation 10 22 and this is simply test telling us that the 10 general acceleration is equal to the angular acceleration multiplied by the radius. So this would be 14.2 radiance per second squared multiplied by 2.83 centimeters and this is giving us 40.2 centimeters per second squared. So this would be your answer for party. Ah, we can then say that the angular velocity is equaling 27 60 revolutions per minute. Times two pi radiance for everyone. Revolution multiplied by one minute for every 60 seconds. This is giving us 289 radiance per second. And we can say then that the radio acceleration ah would be equal to Omega square times are or 289 radiance per second. Quantity squared, multiplied by again. We can say 0.0 283 meters. We can actually convert kilometers now, and this would be approximately 2.36 times 10 to the third meters per second squared. So this would be your answer for part B. And for part C, we can find the angular displacement so the delta theta would be equal to Omega Squared, Divided by two Alfa. This is simply from the equation. 10 14 and this is equaling 289 radiance per second. Quantity squared, provided by two times 14.2 radiance per second squared. This is giving us 2.94 times 10 to the third radiance. And then we can, uh, essentially find using equation 10 won the distance traveled. So this would be asked equalling our times Delta Fada or are being 0.283 meters multiplied by 2.94 times 10 to the third radiance and we find that the total distance traveled is 83.2 meters. This would be our final answer for part C. That is the end of the solution. Thank you for watching.

Sarah Mccrumb · Answer

everybody. So we need to find a really a Radius. And Rossi, times are so for this we have data equals the lost not finds time at plus 1/2 segregation squared, and it&#x27;s used 12.0 1/2. And our celebration is giving us three to get square Now was unsolved. He sported a neat 12.56 1.5. I&#x27;m not using units because it makes it so much year for me to write this out without can cramps by if it helps you always right out unit. Okay. And so now? No, but this here, initial waas the tea and again because you&#x27;re confined its period glossy. And a Sunni zero plus 3 2.9 seconds. And this should give you, um and a three is radiant. Second squared away. Okay, So because of this, what you get is 8.6. Well, it&#x27;s second hurt, And now we could find a grad. Yes. OK, pools, your recon squared are so I&#x27;ll write out units. Eight points, e ingredient second. Yeah, this is squared and were given zero point. And this is gonna give us clean seven meters. And now for the We are given the really hip of a greedy INTs glossy, scared of our Okay, me friend, be his are may God. So again got 8.6. And I&#x27;m like this. And this is devise wine. A 0.7 seconds. Okay, I am in for Avians here. 1.76 where he expired by zero point. You and this is gonna give ours being a 0.68 Here&#x27;s the second split. Okay. Thank you, guys.

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Three masses are attached to a 1.5 m long massles…

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