5

(10) Rolling 5 motion- without slipping- is & combination of translational and rotational motion: (2) Do one complete roll of the wheel on the ground and calcul...

Question

(10) Rolling 5 motion- without slipping- is & combination of translational and rotational motion: (2) Do one complete roll of the wheel on the ground and calculate the velocity of point 0, the center of the wheel, relative to the ground in terms of r and @. (you have to explain your steps). (b) Apply the concept of relative velocity tO figure out the velocity of points A and B relative t0 the ground (again in terms ofrand @) (€) If @ is Xx rad/s, and [ = xX cm, what is the value of the vel

(10) Rolling 5 motion- without slipping- is & combination of translational and rotational motion: (2) Do one complete roll of the wheel on the ground and calculate the velocity of point 0, the center of the wheel, relative to the ground in terms of r and @. (you have to explain your steps). (b) Apply the concept of relative velocity tO figure out the velocity of points A and B relative t0 the ground (again in terms ofrand @) (€) If @ is Xx rad/s, and [ = xX cm, what is the value of the velocity at the specified points A, B. and 0. (10 points)



Answers

A solid sphere is set into motion on a rough horizontal surface with a linear speed $v$ in the forward direction and an angular speed $v / R$ in the anticlockwise direction as shown in figure (10-E16). Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.

Under everyone here it is given of real rules. Without selfie on, the six cylinder is rolling without sipping on fixing the brilliance of the village. Given 40 millimeter. That is why, you know, poured meter over the cylinder operate. It's once it's two millimeter. That is why 16 m motion off. I mean, you're ruling and bullet, but the city or village given then Raelian particle A lot of my direction. So my money we always use this san convention. We're back connotation. This is K Cup. This is I kept on. This is Jacob. So this isn't broke my direction. That's why it is minus kicker and with an acceleration of it is given 30 or really in particular square contract Rock bite. So let's cake. We have to fight Elephant park acceleration off. It wouldn't be point and shipping acceleration off a acceleration off the on acceleration. Upsy that we have to help may start solving it. First, we will do velocity analysis for rather city analysis. Veto. We will find, See is a spiritual center of the village. See, it's been in years. Send it off the big bro cation and the city off a point will be on into a medium. Are you get the areas of the village when you dont put me too. May God has given can't really In Parsippany Square, you will get quite foot meter per second. Velocity off is why would be tougher. Second along right direction, no acceleration And it is quite a moves in a circle or radius. Now we will do acceleration Analysis. Why a If you see a difficult point A movie moving in a circuit offer Idiots are lesser. That is why. 16 let's quite, you know, put 0.2 m. Okay, since the real consensual it so it's a horizontal acceleration will be, You know, it may have a collusion and vertical direction. No acceleration off. See point when we find it in terms off you see candidates acceleration off and insult acceleration off. See with respect week Normal exploration Upsy been, respectively. No acceleration off a Is he already evident? Issue Jacob Acceleration off A In the insurrection minus, I kept Norman activation off. The density off is square upon its in medias. And that will be minus Jacob. So this is that religion off it Not unusual acceleration. Upsy are you doing? A law? Right? Direction. So you get Let's meet. Square up along by exists. No, simplify it. Is he Jacob Gambardella acceleration or be along Pain Angel direction. I am Bennett City. Off is white foot. It really is. Is why do minus Gica Well, really? It's. Intervene it. Why? I'm beautiful and plays 30. Really? Is it while I'm beautiful and anglers veracity sped on. Simplify this equation. Human right and acceleration orbit. Unusual company. I can and then you solve it. You will get minus point it, Jacob this trump and we simply fight you will get. But why do are you kept? But let's full Jacob so on you could be x component and by company, off every question according to x component you will get. That is tangential acceleration off a point, you will get 1.2 m per second squared. And if the e quick the white component of this execution you will get. Is she? So you 0.0, meet up our tech industry. So acceleration off a part of it. Inviting the un perro part eight acceleration off e can belittle is 1.2 minus. I kept the less. Why? Inch minus gica. Meet up for second square. So this is the one of bouncing off this problem. Acceleration off the point part of me, Ben. But it is acceleration off. It acceleration off me. With respect. Okay, Venusian acceleration off me is respectful thing. No. What? This value is minus one point. Do I kept minus point in Jacob? This is acceleration off acceleration. Then you tell activation off me. Okay, guys. And play into what? So what do you know? Pull into 30. Direction is minus Jacob. Normal exhibition or be very square. We got to spend. Where did you don't put I on? Simplify acceleration off. Three point. You will get two point in icam tu minus. Jacob, meet up our second square. So this is the onset off. Be part no, on the autopsy. Already we have. Major. Is he Jacob on a C is three point their support. This problem. Thanks for watching it

This problem goes the concept of the relation between the rotational and translational motion. Since the Will A. And B are connected with about B. Therefore the translational acceleration of A. That is A. T. A. Will be cuba into the translational acceleration of. See that is the financial acceleration of A. And B will be equal. And we can write a tangential acceleration for years. The radius of eight times the angular acceleration of A. And that is a Cuban bento, the release of C times the angular acceleration of C. Now from this we can right the angular acceleration of seas, the radius of A. Upon the radius of sea into the angular acceleration of A. Now we can calculate the angular acceleration by subjecting the value so Alpha C. Equals the ideas of is 10 centimeter And that is of sees 25 centimetre Into the English acceleration of A's 1.6 Radiance for 2nd Square. So al Fassi equals 0.64 Radiance for 2nd Square. Let's say this is a question. Now, the final angular speed of the desk. See that is w do see is 100 revolutions four minute. And we have the angular acceleration ingredients for 2nd square. Therefore we need to first convert the angular speed into radiance Paszek and therefore we need to multiply with to buy radiant poor revolution into uh one minute for 60 seconds. Are the final english speed of the succeeds 10.5 radiance or second. And whenever the time is a cuba until the final english speed managed the initial english speed upon the angular acceleration Africans secured, the values of T equals The final regular speed is 10.5 radiance force again and the initial angular speed for rest is zero. So 10.5 minutes, zero radiance four seconds Upon the angular acceleration. Alpha, that is 0.64 Radiance or 2nd square. So the time tears 16 seconds. So it will take 16 seconds to reach the angular speed off 100 rpm for disc. See

Problem we have given a mechanical were initially addressed on the floor begins rolling forward with an angler Excavation of radiant 1st. 2nd, If the areas of real is 0.5 metre radius is given 0.5 m. What is the linear velocity of the wheel? After five seconds? Time will is five seconds and we have given the angle acceleration Alpha is equal to And the England exploration is given to radiant 1st 2nd square. So, first of all, we will find the angular speed after five seconds. So we will use charismatic equation will make a final is equal to make the initial place Alfa into time It is zero alpha is two and time has also given which is equal to five seconds. So this is equal to 10 radium First again, sister angular velocity after five seconds. Now we know that we is equal to omega into our So this is 10 and the aliases given which is 0.5. The linear speed will be equal to five m per second. Now we will check the options. So here option c will re correct option right of senses, correct

The linear velocity or for real, this region Daisy is a call to a radius Time made out. We're where we need Ah, Mega R is given So the Omega is a call to initial maker. We'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'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.


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