<p>Uh, isn’t that how they taught pendulums? At least in my class they did - like, set the two values for torque equal to each other, and you get that differential equation where sin(theta) = theta.</p>
<p>Lol wow I think I got 0-1 points on the 2nd FR for Mech. Did poorly on #3 too. and skipped part D of number 1…LOL
but MC was easy. hopefully that’ll bring me up to a 5.</p>
<p>E/m was so hard, I think I got like 1/4 of the total points on the FR. MC was killer too, cause I didn’t study anything. Hoping just to pass with a 3.</p>
<p>yeah my teacher barely went over pendulums at all, let alone physical pendulums… and they never even mentioned a physical pendulum in the princeton review book (which was very good nonetheless) so I never bother to memorize the T= 2<em>pi</em>sqrt(mgd/I) which only 2 kids in my class remembered.</p>
<p>Hmmm we didn’t talk about physical pendulums much either. I stared at it for 5 minutes and then moved on to #3. I finished #3 and came back to stare at it for 10 minutes before figuring out what was going on <_< lol.<br>
I saw the “small angle approximation” in the second part and knew there had to be a sine function in there, since cos x = 1 wasn’t really likely to be used. So then I thought about torque and then I had I d2theta/dt2 = mgxsin theta and it came out :)</p>
<p>No, we didn’t learn pendulums and oscillations in that much depth. We just barely skimmed over it and our teacher assumed that we could manage problems involving those because there’s only two formulas to memorize.</p>
<p>On the day of the test (in the morning), our teacher gave us the formula for a physical pendulum (we didn’t even know physical pendulums existed until then). And yes, it was that formula (T = 2pisqrt.(mgd/I)), but even if you know that, you need to use the second-order differential to derive it.</p>
<p>Sharvas, did you have a full-year mechanics course?
We had only one semester mech and second semester E&M.
I don’t think any of the students or teachers expected a FRQ like that…</p>
<p>The problem with the test was that it was to abstract and some problems were very vague (like Mech # 2). Take a look at 2008’s test: They had basic problems like F=ma for an inclined slope, simple Kirchoff circuit loops, loops moving in magnetic fields, Gauss’s Law for two simple enclosing spheres…
And this year we don’t get a single straightforward question.</p>
<p>Now we can discuss the free response freely! 
Collegeboard even put up original question. I still don’t know how to do No.2. Paralell Axis Theorem perhaps?</p>
<p><a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
<p>Torque = F x R = mgx sin ϑ
And torque = I d2ϑ/dt2</p>
<p>So use the small angle approximation sin ϑ ~= ϑ and solve the second-order differential equation</p>
<p>Yea #2 was very weird… and I was surprised at #3 too since our teacher “mentioned” those types of problems but we never did one so I thought we would never get one on the test… but it wasn’t that bad, #2 was much more difficult conceptually trying to figure out what the heck they want</p>
<p>A lot of talk on #2. But, how did you get the graphs for #1? I had no idea how to convert equations in terms of x into an equation in terms of t, which was needed for both graphs.</p>
<p>were the speeds the same for #3(e)?</p>
<p>^Yes 10char</p>
<p>how many points do you think the graph for #1 was worth? hopefully only 3 but maybe more</p>
<p>
</p>
<p>No, I had one semester of mechanics and one of e&m. But maybe my physics class was just pretty good (I took it through EPGY). But maybe that’s why Princeton Review didn’t mention it at all. I thought it was pretty important though.</p>
<p>What was your reasoning for the same speed on #3?</p>
<p>Same here, I messed up on #1 graphs too. I would’ve probably got it if I spent more time on it…I skipped it and quickly sketched something in literally the last minute.</p>
<p>I even messed up on the E&M #1 graph. What did that look like for you guys?</p>
<p>@athenos: If you solve for v in both, you get the same thing.</p>
<p>On the first e&m were they both radially outward?</p>
<p>^^No, the first one was radially inward.</p>
<p>@ data and Senior0991</p>
<p>For mechanics #3 I got:</p>
<p>a) sqrt(gd)</p>
<p>and d) sqrt(2gl)</p>
<p>So for e) I put that the rope moves faster because it’s velocity is greater by a factor of sqrt(2).</p>
<p>A lot of my friends used energy for 1a) and I don’t think they did it right. I used net force equations and ended up with an acceleration of (g/2). I hope I did it right…
Any input?</p>
<p>What, really?
Tons of people I know (including me) used energy and got the velocities to be equal.
I was totally sure I got that right after confirming it with so many people from my class. </p>
<p>I did try forces before using energy, it didn’t work out right (there’s nothing pulling against the rope…frictionless table).</p>
<p>The way I saw it: :D</p>
<p>Netforce one hanging = (m/2)g - T = (m/2)a
Netforce on sliding = T - u(m/2)g = (m/2)a ; u = 0 so T= (m/2)a
Substituting T into equation #1 yields a = g/2
from that acceleration one finds that v = sqrt(gd)</p>
<p>Oh yea, learned this stuff earrrrrrrly in first semester…the acceleration is ALWAYS less than g in cases as such (not all!)</p>
<p>Wait a min, how can you even do F(friction) = uF(normal) if the table is frictionless?
There’s no tension or friction on the sliding rope…</p>
<p>Yes, the acceleration does end up being less than g, but the velocities ARE equal I thought?</p>