Angular acceleration - in over my head!

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Sarissa
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I'm doing a year 2 engineering course at the moment and i'm finding it a massive jump up from year 1 with little in the way of help to bridge the gap. At the moment we're covering angular and curvilinear motion and i'm struggling to follow it. I'm going to post some shots from my text book and hopefully someone can explain to me where i'm going wrong...

I don't know how to edit it to put the pic next to the question i'm asking, so i'll just number them.

Pic 3.2 + 3.3: Starts with an equation i don't really understand. "1- exp" it's not explained what the 1 represents, and it doesn't explain what exp is or how to calculate it. I first thought it was exponential, but that didn't seem to fit either. The second part is -t/tau, but all i get from this tau is equivalent to t when terminal speed is reached? Part way through 3.3 there's an example, but i can't get my results to match those, probably because i don't really understand what i'm doing.

Pic 3.3 and 3.4: Contain 2 questions. The first one is asking me to calculate when angular speed is 0, but how can i do that if they don't give me the power at which the rockets are firing?

The second set of questions on 3.4 is something i can't begin to answer because i haven't understood the preceeding section. But it also gives me some graphs to fill in, but the text book has only shown me angular speed graphs, how would i fill in the other 2 graphs?
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Sarissa
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Just looking at how the pics have loaded, and they're not in order. The order they appear in (to me) is 3.2 , 3.4 , 3.3. In case that confuses anyone.
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Sarissa
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Anyone?
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Zacken
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(Original post by Sarissa)
Pic 3.2 + 3.3: Starts with an equation i don't really understand. "1- exp" it's not explained what the 1 represents, and it doesn't explain what exp is or how to calculate it. I first thought it was exponential, but that didn't seem to fit either. The second part is -t/tau, but all i get from this tau is equivalent to t when terminal speed is reached? Part way through 3.3 there's an example, but i can't get my results to match those, probably because i don't really understand what i'm doing.
It's saying that w = w_0 (1 - e^(-t/tau)).

exp(anything) = e^(anything) it does work.
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almostmaybe
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(Original post by Sarissa)

Pic 3.2 + 3.3: Starts with an equation i don't really understand. "1- exp" it's not explained what the 1 represents, and it doesn't explain what exp is or how to calculate it. I first thought it was exponential, but that didn't seem to fit either. The second part is -t/tau, but all i get from this tau is equivalent to t when terminal speed is reached? Part way through 3.3 there's an example, but i can't get my results to match those, probably because i don't really understand what i'm doing.
You were right exp(x) means e^x. So you are raising e to the power of everything inside the brackets. If you do that, it should work out.

What you have is the mathematical model that gives the curve shown in the graph. If you substitute t = 0 and t = \infty into the equation, you'll see that you get 0 and the terminal velocity, respectively.

It's hard to give an explanation for what the '1' means, except to say that this is the mathematical expression that gives the curve. Play about with the maths a bit, see what the curve would look like if the '1' wasn't there and you should get a better feel for it,

Pic 3.3 and 3.4: Contain 2 questions. The first one is asking me to calculate when angular speed is 0, but how can i do that if they don't give me the power at which the rockets are firing?
You have an equation that tells you the angular velocity as a function of time. You can obtain an expression for angular acceleration as a function of time by differentiating this, as shown in the example. Try to work through this to see how it is obtained.

Now that you have this equation, you can simply substitute in the values for terminal velocity,  \omega_0, and the time constant, \tau, both of which you are given for this particular system. Then substitute in the values of t to calculate the angular acceleration at those times.


The second set of questions on 3.4 is something i can't begin to answer because i haven't understood the preceeding section. But it also gives me some graphs to fill in, but the text book has only shown me angular speed graphs, how would i fill in the other 2 graphs?
You can sketch through the graphs by thinking through what is happening in terms of angular position, velocity and acceleration. The following questions are then an exercise in using the equations you have learnt.
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