Wzory kinematyczne ruchu obrotowego. O nas. Transkrypcja. David explains the. mechanika dział fizyki zajmujący się ruchem, równowagą i oddziaływaniem ciał. mechanika klasyczna opiera się na trzech zasadach dynamiki newtona i bada. w opisie kinematyki oraz dynamiki ukła- dów korbowo-tłokowych . KINEMATYKA UKŁADU KORBOWO- jest od kąta α i dane jest wzorem (3), (5). The shift of.
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We could find this area, relate it to omega and alpha and we’d get the rotational kinematic formulas, but we already know since these are all defined the same way the linear motion variables kinematykw defined, we’re gonna get the exact same equations, just with the linear motion variable replaced with its rotational motion variable.
Wzory kinematyczne ruchu obrotowego
You ended up with seconds squared on the top. You get a negative wzry radians per second squared. So this angular acceleration has gotta have the opposite sign to the initial angular velocity. And the closer in you go, the smaller the r will be, the smaller the speed will be. And that’s the time.
kinematyk But we want our delta theta always to be in radians, cause look it, our acceleration was given in radians per seconds squared. We called this positive 40, that means our alpha’s gonna be negative. This third one has no omega final, so Kinematka gonna use that one. Similarly this angular velocity was the angular displacement per time just like velocity was the regular displacement over time. And so because these definitions are exactly the same except for the fact that the linear motion variable is replaced with its angular counterpart, all the equations results in principles we found and derived for the linear motion variables will also hold true for the rotational motions variables as long as you replace the linear motion variable in that linematyka with its rotational motion variable counterpart.
So let’s say you had a velocity versus time graph and it looked like this.
Wzory kinematyczne ruchu obrotowego (film) | Khan Academy
First one’s got omega final. So that was one example. We wanna know the time that it took. And then it’s dzory be plus two times alpha. And then you gotta divide by this two as well kinejatyka the 40 pi radians, which gives me negative 6. The angular acceleration was 30 and the time is what we wanna know. What’s our third known? Let’s say you had a four meter long bar, that’s why I’ve had this bar here the whole time, to show that it can rotate.
Now if you wanted rotational kinematic formulas, you could go though the trouble that we went through with these to derive them using areas under curves, but since we know the relationship between all these rotational motion variables is the same as the relationship between the linear motion variables, I can make rotational motion kinematic formulas simply by replacing all of these linear variables with their rotational motion variable counterparts.
Which one do we want to solve for?
Rzut ukośny (fizyka)
And in this case this is the axis right there. Wzry just kinemmatyka the distance from the axis, to the point that you want to determine the speed and then you multiply it by the angular velocity and that gives you what the speed of that point is.
Let’s do another one. One revolution is two pi radians, cause one time around the entire circle is two pi radians. All right, this one we’re gonna have to actually use a kinematic formula for.
I’ve got my three knowns and my one unknown kinematykaa I want to find. Which variable isn’t involved? It’s gonna be when the alpha, the angular acceleration is constant.
I was neither give the time nor was I asked to find the time.
So let me copy these. And so if you remember from 1D kinemtyka, the way we derived a lot of the 1D kinematic formulas that related these linear motion variables, was by looking for areas under a velocity graph. This is in units for revolutions.
You always need a third known to use a kinematic formula. So that means that the area under the curve on a omega versus time graph, an angular velocity versus time graph is gonna represent the angular displacement. So for instance, this angular displacement was defined the exact same way we defined regular displacement, it’s just this is the angular position as opposed to the position, the regular position.
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So these are gonna travel, these points on the rod down here don’t travel very fast at all, because their r is so small. They’re all rotating with the same number of radians per second, but the actual distance of the circle they’re traveling through is different, which makes all of their speeds different.
Again the way you use these, you identify what you know. So in other words, this point on the bar right here, is gonna have some velocity this way.
Similarly the area underneath the curve on a velocity versus time graph represented the displacement. But that’s only two rotational kinematic variables. Then we divide by The are only true if the angular acceleration is constant, but if it is constant, these are a convenient way to relate all these rotational motion variables and you can solve a ton a problems using these rotational kinematic formulas.
And that’ll end up giving us 20 pi, and technically that is 20 pi radians divided by 30 radians per second squared and then you have to take the square root, because it’s t squared. We know omega final was zero.