Cambridge Maths Tripos Exams

OP

smilepea

Hopefully education with something nice (what the nice thing will be is yet to be decided!)

Haha, have you narrowed it down to a few choices yet :p:

?

Ahhhhhh, paper 4 tomorrow, yuck...

Reply 62

Hmmm hmmm, perhaps it was not a good idea to put off Dynamics until now.

Either that, or I'm being stupid. How does one get from

\displaystyle \left[ \sec \frac{1}{2}\theta \right]^4 \frac{d\theta}{dt} = \frac{h}{{r_0}^2}

and

\displaystyle r = r_0 \left( \sec \frac{1}{2}\theta \right)^2

to concluding that

r = 2 r_0

when

t = \frac{8 {r_0}^2}{3 h}

? (Q11, 2007) Even Mathematica doesn't seem to be too happy to do the integral, and Siklos's comments seem to suggest that it can be done by other methods, but I'm not seeing how to get the kinematic equations.

Reply 63

squeezebox

15

Zhen Lin

Hmmm hmmm, perhaps it was not a good idea to put off Dynamics until now.

Either that, or I'm being stupid. How does one get from

\displaystyle \left[ \sec \frac{1}{2}\theta \right]^4 \frac{d\theta}{dt} = \frac{h}{{r_0}^2}

and

\displaystyle r = r_0 \left( \sec \frac{1}{2}\theta \right)^2

to concluding that

r = 2 r_0

when

t = \frac{8 {r_0}^2}{3 h}

? (Q11, 2007) Even Mathematica doesn't seem to be too happy to do the integral, and Siklos's comments seem to suggest that it can be done by other methods, but I'm not seeing how to get the kinematic equations.

When r = 2r_0, theta = pi/2. So integrate the differential equation from theta = 0 to pi/2 and t = 0 to T.

Edit: if it's the integral, surely

sec^{4}(\theta/2) = sec^{2}(\theta/2)( tan^{2}(\theta/2) + 1)

knocks it on the head?.

Reply 64

That works. It's a bit unsatisfactory though... I was obsessing over how to get from the time to the position, which appears to be somewhat more difficult, and didn't think about going the other way.

Tunnel vision is dangerous. :-/

Reply 65

Slumpy

Just as a thought, anyone else feel screwed for tomorrow?
Two of my worst three subjects together, and on my birthday!
Any tips anyone? :p:

Reply 66

For SR: Use 4-vectors. They will make work much easier. Also, make sure you know what

v

is associated with each

\gamma

...

Reply 67

OP

Slumpy

Just as a thought, anyone else feel screwed for tomorrow?
Two of my worst three subjects together, and on my birthday!
Any tips anyone? :p:

Hehe, let's hope it's a nice one for your birthday :smile:

. I'm hoping for a collisions question in the special relativity part ^_^ ...

Reply 68

smilepea

Simba

Haha, have you narrowed it down to a few choices yet :p:

?

Ahhhhhh, paper 4 tomorrow, yuck...

It's more dependent on what they're happy to let me do, I have a few ideas but we'll wait and see :smile:

time to go and lean the proof of the IEP ...

Reply 69

Gah, Dynamics did not go very well. I don't know how, but I calculated that the punctured disc would experience friction in the forward direction. Somehow that seems counterintuitive. And I can't believe they actually gave us 2 long SR questions... although I only did one.

N&S bothers me as well. Q5 seemed too easy... :-/ And I just realised I didn't explicitly prove that the reals were uncountable. Gah.

Reply 70

OP

I thought on the N+S section was easier than previous years by quite a bit, and the dynamics/relativity was pretty nice as well. That's the best paper 4 I've ever done :p:

, which is not saying a lot...

Reply 71

harr

15

Zhen Lin

And I just realised I didn't explicitly prove that the reals were uncountable. Gah.

Same for me. Read it when I first looked through the paper, forgot when I actually did the question. At least I managed to prove that k(p choose k) is divisible by kp.

I haven't used any puns in this post, but here are some I could have used:
Probability -- Stadistic
Tsiolkovskii equation -- Using a nutcracker to crack a nut

Reply 72

DPMMS: Department of Pure Mathematics and Mathematical Sadistics.

At least according to Dr Bursill-Hall...

Reply 73

harr

15

I obviously need to work on my originality... I would hope that the other joke hasn't had any previous widespread use though.

I've now got my first neg rep: "This is because I can't be bothered to go upstairs and kick you."

Reply 74

Whoo, it's all over!

Except it's been pointed out to me that my solution to Q9 is fundamentally invalid because there is no divergence theorem in 2D. Bah. So that means Q10 is my only good VC solution... :s-smilie:

Reply 75

OP

Zhen Lin: Errr, there is a divergence theorem in 2D.

Nasty, nasty paper overall I thought. Glad it's all over, time to relax and play poker :wink:

.

Reply 76

generalebriety

What the **** was that.

Reply 77