Tuesday, November 11, 2014

Revision Note 1: Vectors and components of vectors

There are two ways to represent a 2D vector, v:
1.       (v, θ)
·         v is the magnitude of the vector v.
·         θ is the angle that the vector’s direction makes with the x-axis.
2.       v = vxi + vyj
·         vx is the x-component of the vector.
·         vy is the y-component of the vector.
The second representation is more convenient for problems. An intuitive connection between the two representations is this: The vector v can be represented by an arrow drawn from (0, 0) to (vx, vy). In that case the length of the arrow will be v and it will make an angle θ with the x-axis.  

Problem Solving Tips:

Tip 1.1:
Drawing vectors: Put the tail of the arrow at the point of application – e.g., the arrow representing a force vector, F, should have the tail on the body on which F is applied. A common mistake (especially for force vectors) is to put the head at the point of application.

Tip 1.2:


Going from (vx, vy) form to (v, θ) form:


Tip 1.3:
The component of a vector v along a certain direction is v.cos θ where θ is the included angle between the direction of the vector and the direction of the component.
This is the “shadow = cos θ” tip. (shadow = the component of the vector with sun at noon.)
The component perpendicular to the above is v.cos (90-θ) = v.sin θ.

Tip 1.4:
The component of a vector along a direction perpendicular to itself is 0. This principle of orthogonality is used to simplify problems.

Tip 1.5: Up-down intuition:
As the angle θ that the vector makes with the horizontal increases from  to , the horizontal component vx decreases. The arrows in the notation represent this relationship. The relationship vx = v.cos θ is not exactly linear.

θ ↑ vx

Monday, November 10, 2014

Revision Notes for Physics C

Hi everyone! In this blog I’ll be posting my tips, advice, and notes for the Advanced Placement Physics C – Mechanics exam. Hopefully these posts will benefit people preparing for the exam! You can read through the posts chronologically (as I’ll be covering all the major topics) or pick and choose the notes you need.

A big disclaimer: I haven’t yet taken the AP Physics C exam, so I’m not sure if all of this works. I’m writing this blog as I’m preparing for the exam, so these notes are the ones I’ll be using to prepare myself. If you find any errors, do let me know! My goal is to make this blog into a collaborative learning blog and help others like me who are taking this exam.

A smaller disclaimer: This blog covers just the main concepts relevant to Physics C – so not every Physics concept is covered.


So, without any further delay, let’s get right into the syllabus. Welcome to your Physics C journey! J