Oxford University Mathematician takes Oxford PHYSICS Admissions Test (PAT) - with @zhelyo_physics

University of Oxford Mathematician Dr Tom Crawford is challenged by Zhelyo from @zhelyo_physics to try some questions from the Oxford Physics Admissions Test (PAT). The exam is taken by students applying for undergraduate Physics at the University of Oxford.

The questions covered in the video are as follows:
Q1-10: multiple choice
Q18: gravitational force

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

With thanks to
Zhelyo @zhelyo_physics
St Edmund Hall
University of Oxford Department for Continuing Education
Freesound: Rich Craft Chime
Freesound: Suicdxsaturday

[DavidKrech-du]

Hey! I am 50 years out of college but I love the content. You Gentlemen are enthusiastic and you have fun. I love math and science. Thank you for making my day. When you love what you do, you never work a day in your life. Hope to see a lot more. ENJOY😊

[LithinHariprasad-vgyr]

FIRST TIME LOOKING AT A PERSON WHO STRUGGLES IN PHYSICS BUT WHO IS ACTUALLY AN MATHEMATICIAN

[felixkersey]

You said at the end that you hadn't stopped smiling. I honestly feel like you are always smiling in your videos! It's really cool to see someone so excited and in love with the subject!

[zhelyo_physics]

Looking forward to seeing the edit on this! So much fun to film!

[andrewgilday]

Great work Zhelyo (and Tom)! Looking forward to doing some of these with our students when we get back to work!! Have a good summer!

[copywright]

There's definitely a very big difference in philosophy between physics and math profs for making test questions, probably comes from the differences in philosophy and mindset of physicists and mathematicians in general

[ericerpelding]

Hidden in the solution of the gravitational hanging spheres problem is the approximation tan(theta) = sin(theta). This is acceptable as the angle will be small.

[monkerud]

You can think of force as equivalent with the gradient of a potential. If the gradient is zero, there is no force, if the gradient is not zero there is a force. When the ball is hanging at an angle, it is hanging straight down the gradient of the combined potential. Now we know that the ball will not hang around in any other location, and so it must be the only place where the potential and mechancal force on the rope are parallel, equal and opposite.

[DylanNelsonSA]

You do have to consider the tension from the rope because there is no "horizontal component of the gravity". The horizontal component that is balanced with the gravitational force between the two spheres is the horizontal component of the tension. The vertical component of the tension is equal to mg, so the horizontal component is mg tan θ. Here we then use the assumption that δx << L to approximate tan θ as sin θ = δx/L. (Since we actually have tan θ = δx/√(L^2 - δx^2))

[forthrightgambitia]

For question 4, I would have just used the mean of the binomial distribution np. If p is the probability of turning left, the np = 3/3 = 1. So the mean number of turns left is 1, which means 2 turns right. Or you can say p is the probability of turning right, so 6/3 = 2, 2 turns right 1 left as well. And that is C.

[jacobharris]

For 6 I was really confused why both of you didn't chose A until I realized I had read the question wrong and the string was fixed in the middle. For 7 I used calculus to derived one of the kinematic equations and used that because I couldn't remember it but the energy approach is much simpler.

[zidaneismail]

Hey Tom. I am from South Africa and a huge fan. Would love to see you sit a South African high school exam.

[monkerud]

Sum the potentials and take the gradient, which position along the balls freedom in position does the ball hang parallel to the gradient of the potential.

[alhassanedembele]

La combinaison la plus probable est donc d’aller à droite deux fois et une fois à gauche, avec une probabilité de 12/27❤❤❤

Solution :
Pour résoudre cet exercice, nous devons trouver la valeur maximale de ( a ) telle que la somme des quantités de thé ne dépasse pas 3 fois la quantité de la première tasse.
La quantité totale de thé bue est une série géométrique :
S=1+a+a2+a3+…
Donc a< ou égal à 2/3
❤❤❤❤
Je fais la licence 1 en informatique mais je trouve tes exos sympa

[omicronl]

I guessed that it was C with other reason

By the Definition, two thirds will Go right and one third left, that means the most likely combination is going twice right and once left (Sorry for my english)

[ayo]

came at a perfect time! i was actually planning on checking out some of the pat questions to get used to them and see if my level is worth applying :)

[GeekRedux]

I don't think question 2 5:26 is correct. The trajectory 2 is a valid trajectory. But using the scale values, we can see two other trajectories are ruled out:

The ellipse, 1, should have it's closest distance along its major axis at approximately (-3, -3.5), which is at a distance of about 4.61 from the star. But there are two closer points at about (-2, 3) and (2, -3), each about 3.6 from the star.

The parabola, 4, should have its closest point to the star along its axis of symmetry at (0, -2) at a distance of 2. But two points at about (-1.1, -1.1) and (1.1, -1.1) are each only about 1.55 from the focus.

It's hard to tell with the hyperbola 5, but it looks like its closest point is on its axis of symmetry and is therefore a valid trajectory.

But, using the provided scales, trajectories 1, 3, and 4 are all invalid trajectories. The correct answer isn't an option.

[Ferraco]

39:00 literally the exact same reaction I get from my maths friend when I tell him something like this 😂

[jacobharris]

That's a pretty complicated set of units you put on screen for voltage but I can see that the units work out. I just think of it as energy per unit charge or Joules per coulomb. If I forget that, which I did for the third question, I just recall the integral definition of voltage and the units of N/C for an electric field to work it out in my head. If you forget the units of electric field but remember Coulomb's law and F=qE (Lorentz force law without magnetic field) then that's also easy to quickly work out in your head. The relationship between electric field and voltage is similar to the relationship between force and potential energy (or the amount of work required to travel somewhere from a chosen reference point, often infinitely far away for a system with only central forces). The relationship between electric field and force is similar to force and acceleration with charge being the bridge between them, instead of mass.

[arrans_autos]

Hi Tom, another great video! Just out of interest, what iPad app do you use for note taking?