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...