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Kuln_(heolrotating_abouF #I Q fixed , axic 8cct"6atokckt 4USorataa cons Ingfa " angular t0 radius = 0.30m find angular velocity #IL +2 sume info find seco...

Question

Kuln_(heolrotating_abouF #I Q fixed , axic 8cct"6atokckt 4USorataa cons Ingfa " angular t0 radius = 0.30m find angular velocity #IL +2 sume info find secondc Cpith

Kuln_ (heolrotating_abouF #I Q fixed , axic 8cct"6atokckt 4USorataa cons Ingfa " angular t0 radius = 0.30m find angular velocity #IL +2 sume info find secondc Cpith



Answers

(a) Derive an equation for the radial acceleration that includes $v$ and $\omega,$ but not $r .$ (b) You are designing a merry-go-roundfor which a point on the rim will have a radial acceleration of 0.500 $\mathrm{m} / \mathrm{s}^{2}$ when the tangential velocity of that point has magnitude 2.00 $\mathrm{m} / \mathrm{s} .$ What angular velocity is required to achieve these values?

This question were given that there is a well of radius 14" and starting at .5 radiant per second. This is radiant per second. Where's a linear speed as once the linear speed as uh omega times the radio. That straightforward formula. Omega has already given us 0.5 reading per second and the radius has given us 14. So that's gonna be seven, seven m/s. So that is the linear speed. Uh Then in part B they're talking about the angular rpm. So that's where we need to do some calculations because we're given that at the speed is point by radiant per second RPMs, revolutions per minute. Now in in two pi radiance into pie radiance, there is one revolution. This is equal to the one revolution because one revolution has two pi degrees covered to buy radiance covered. So in 20.5 radiance in 0.5 point five radiance, the number of revolution is going to be 1/2, 5 times. 0.5. So that will be in revolutions per second because uh the angular speed isn't 0.5 gradient per second. But so this is nothing but zero point 5/2 5. But we are interested in Revolution per minute. So if we have to convert the second two minutes and we have to multiply and about 1/16. So that's gonna be equal 2.5 over two pi and uh 2nd 2nd will be converted as 1/60. So that's in minutes. So the 60 comes on top. So we have, we multiply. I've got to use the calculators here. Uh that's gonna be equal to 60 times. It's going to be equal to 16 divided by two divided by fire. Nobody did by 0.5. So that's going to be equal to 477 R. P. M. And and part C. We have to find the angular speeding degree parade ian's and degree parady in. So that's an easy conversion. Uh We know that uh by radiance is same as 1 80°. So the speed has given us 0.5. So 0.5 radiance has got to be 1 80/5 times. 0.5. That's gonna be degree, that's gonna be degree and per second as anyway as it is. So let's simplify this. That's going to be equal to 90/5. Just 28 0.65 degree per second. So this is the required answer for uh box. See Thank you.

In this problem we have given the guys equals to 12. Spy Radian on time is equals to 55 seconds on were asked to find the angular velocity off point p By the definition of angular velocity we have angular velocity is equals to take it up on T. Now we will substitute 12th fire raiding for theater and 55 2nd 40 we get angular. Velocity is equals to 12 By raiding upon 55 seconds, it would be equals toe 12 radiant upon five seconds. I simply find it. We get 2.4 radian per second. Therefore we get angular. Velocity off point P is equals to 2.4 radian per second.

We have as, uh, he's given by centripetal. Acceleration is went by our now we'll make odd. That's only go now. Only God is V again right as you go. So we would have Oh, my God. It was It is the accident. Ation. So acceleration over that awesome be speak once. 0.5 or 12 It was a 120.25 ready in the second.

Mhm. This problem covers the concept of the rotational kinetic energy and the rotational kinetic energy equals half of the moment of Tunisia into omega squared. And from this equation we can write omega equals squabbled off two times the rotational connect technology upon the moment of us. Here. Now let's substitute the value. So omega equals square root off two. And to the rotational current technology is 2.75 jewels Upon the moment of necessity, 0.33 kilogram meters square. So the angular speed or my guys 4.08 radiance for second. Now we need to find the omega into revolution. Permanence. Omega equals 4.8 radiance for second into uh one revolutions for two pi radian into uh 60 seconds for a minute. So the angle speed omega is 39 revolutions for a minute.


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