I would have to disagree about the matrix algebra class, at least compared to my experience. At uvic, there are 2 matrix algebra/linear algebra courses, one is geared towards the engineers and IS primarily applied linear algebra, but the one that is required for physicists is very proof-based...
Actually it does. If the NET force acting on an object does NONZERO work over a certain time or distance, that is equivalent to saying that the body accelerated. Consider a point mass where two forces are being applied on it, each in opposite direction but equal in magnitude. Using the same...
If you are willing to assume initial launch height is zero or negligibly small...
θ=(1/2)arcsin(g*x_max/v^2)
=arcsin[sqrt(2*g*y_max)/v]
t_flight=2*sqrt[2*y_max/g]
Otherwise it's ugly. I see mathematics as both an enabler and a disabler, in your problem it is definitely the latter :(
Let me try and justify this for you.
Let f_2 be the force acting at greater distance from axis, and f_1 acting from the smaller distance.
K=∫(ƩF dot dr)
=∫((F_2-F_1) dot dr)
=∫(F_2 dot dr)-∫(F_2 dot dr)
Consider both of these forces acting tangentially and for a quarter revolution...
I modelled something similar earlier this summer. The method I ended up using is really easy.
Your program needs the inital x, y, and z components and the inital v_x, v_y, v_z components. For each time, you want to find what the acceleration is using a = (GM)/(x+y+z)^2.
Once you have that...
Haha I torture myself over the exact same issue on whether or not I have a mathematical mind. The proof in my textbook for it is entirely algebraic and doesn't make much intuitive sense as say, a graphical reason would.
My advice to you is to stop romanticizing your situation.
The university system does not suffer from teaching in an ancient paradigm the way that high schools are criticized of doing. They are quite modern, but you will have to put up with a chalkboard. And if you think that's dull, try...
In A), you can't move the force to C, because then what force would supply the torque? In other words, torque costs force.
But what I don't know is how much of the force is given to create rotational motion and how much is given to create linear motion. It certainly will depend on time.
EDIT...
first of all, the accerlation the ball feels if it were to move in circular motion with radius (r/2) would be a = 2rw^2
second, if you drop ball directly onto the disc, ie. the trajectory of the fall is perpendicular to the plane of the disc, then the ball would not move, because you told us to...
I mean that those courses require a lot of time, regardless of whether you think the material is easy. But given the amount of time you say you're studying, you should be able to do it. However I noticed you didn't take into account labs. Expect to spend 5-10 hours on each lab.
The air is exerting a force that is equal and opposite to the force of gravity exerted on the elevator. However the speed of the air INSIDE the elevator RELATIVE TO YOU is so small that it would be unable to provide enough air resistance to stop your acceleration. As a result, the elevator stops...
Your last semester looks challenging because you have 3 second year physics courses, which all have a heavy workload and require a large time investment for labs and write-ups. You are also going to be spending SO much time on the physics research course, with pressures of coming up with a...
Maybe try working outside of a 'schedule'. I get the most self-studying done when I just let my curiosity take me places. Yesterday I spent several hours rationalizing why the parallelogram with 2 non-parallel sides being the vectors a and b, is just the det(a,b). Today, I making a program that...
I have the option to take these two computer science courses. Would these courses be useful in my experimental-physics studies? My worry is that they would be too far theorized and that I wouldn't take anything out of the class that I could actually USE to do experimental-physics.
If someone...
Regarding your religious beliefs: there is a small minority of physicists who subscribe to religion, although finding a religious biologist is very rare, and a religious evolutionary biologist even more rare. I'm telling you this more for interests sake than anything else.
the kinetic energy of the falling object is constantly changing because its velocity is changing due to the acceleration due to gravity. You must specify at what location/time you want to know the object's kinetic energy.
I think its much more common for people to want to study galaxies and black holes then 'why bubbles go pop'. If you are unable to see their perspective on why they think its fascinating then you're close-minded.
You'll definitely need another bachelor's degree. Because you already have one major, you'll likely be able to skip the graduating requirements and simply get through the specific program requirements. However, in the first few terms of your new program, your progress will be stagnant until you...
I'm sure most people on this forum would like to make predictions on your 'what if' scenarios, I don't know if it will be allowed though. Some rules on this forum are rather strict, you'll have to wait and see
What it really comes down is money. A first year calculus textbook will have lots of worked examples, diagrams, and graphs along with the text because Calculus I is a gateway class into a bunch of fields so lots of people take it, and so it receives more funding because it has more potential to...