Newton's Problems

Over the past week or two, we learned about four of types of Newton's problems: Equilibrium, Inclines, Pulleys, and Trains. Now, at first, you might be like cause it can get confusing.
Don't worry, though! All you have to do is:
For all the problems, it is important to remember to break down all the vectors into x and y components.
There are also some tricks that can be used:
For equilibrium, remember that the acceleration is always zero, because the object isn't moving. That was pretty obvious.
For inclines, be lazy and tilt your head so you only have to break down one vector instead of two.
For pulleys, remember to draw two free body diagrams and treat the pulley as two systems, not one. Also, the acceleration of the whole system is the same.
Finally, for trains, also break it down into multiple FBDs. Acceleration is consistent, so when trying to figure it out, you only need to draw one FBD and figure it out from there. (:

See? Wasn't that easy? Now you can solve any simple Newton's Problem.

Projectile Motion

"A projectile is any object propelled through space by the exertion of a force which ceases after launch." (taken from wikipedia)

This is a projectile. In order to solve a projectile problem, there are certain things that need to be done. First off, the motion needs to be separated into two parts, x and y. The only thing common between the two is time.
For the x part, assuming there is no air resistance, the velocity is constant, and therefore there is no acceleration.
For the y part, because it is traveling vertically, there is gravitational pull. That means that acceleration due to gravity is always 9.8m/s^2 unless specified otherwise. We also know that whenever dropping an object, v1 is always 0.
By using these givens, it is possible to find any value in y by using the big five. In x, it is possible to solve without the big five.

Roller Coasters!

Time for my favourite roller coaster! I've never actually been on this one, but it's called Nagini's Revenge and it's at the Harry Potter Amusement park. And because I'm a total nerd, I have decided to blog about this one. (: This is the only picture I was able to find of it, which is a bit of a shame, but that's okay.

Looks pretty scary. :P

Adding Vectors

Firstly: What is a vector?
A vector is a quantity that is specified in both direction and magnitude. Vectors possess both a head and a tail, the tail being the start of the arrow and the head being the end of the arrow. Vectors are also written with direction, which can be indicated with and angle, or just a simple [N], [E], [S] or [W] for the simpler vectors.

The notation for the vector on the left would be 20m [N30W].

In order to add vectors, you must look at both the magnitude and the direction. The picture on the left shows how to add vectors that are going in the same or opposite directions. In order to add vectors that are not going in the same or opposite directions, we must use the Pythagorean Theorem. For example, if you have two arrows, one of them being 11km [N] and the other one being 11km [E], the resultant (R) can be found by using the formula a^2 + b^2 = c^2.

But wait, we're not done yet. Vectors have to have both magnitude and direction. We've already figured out magnitude, but now we have to figure out direction. This is explained by the next two pictures: