Review of 8.01L
Prof. Min Chen
9/27/2015
Super-full Moon eclipse tonight at 11pm
Happy Mid-Autumn Festival

Concepts ：
Coordinates: x, y, z or velocity acceleration
r and time t v a
Methods of using the given to find the unknown:
Graphics
Equations
Tools : vectors addition and subtraction,
Calculus: dx n /dx = n x n-1
 x n dx = x n+1 / （ n+1 ） + C
Trigonometry
Taylor series expansion: (1+x) n = 1 + nx +… for x<1
Quadratic solution of ax 2 +2bx + c=0
Law of cos: c 2 = a 2 + b 2 – 2ab cosθ

3-D Position vectors and distances

Given position find v

Given v, compute a

Find a given-v or r vector

Given components find magnitude and direction

801L-2014-Exam1 Problem #2

Projectile with constant acceleration

Relative Motion
P: plane w. r. to air or boat w.r. water
A: air, or water
B: ground/bank

Constant v
Circular motion:
Δs/ Δt=v
Triangle O-P1-P2:
Δs / R = Δφ
Triangle O-v1-v2:
Δv / v = Δφ
= Δs / R
Thus a = Δv / Δt
= v (Δs/ Δt) / R
= v 2 /R (inward)

Circular motion:
Angular velocity ω = v /R = 2πf = 2π/T

Circular motion:

You slide, with zero initial velocity, down a smooth slope from a height H and circle around a large smooth loop with radius R.
What are the accelerations at the bottom and the top of the loop respectively? What is the minimum height H so that you will not fall off the loop? Ignore frictions and air resistance.
H=?
Top
R
Bottom

Physics is fun and useful
Invisible cloak realized!

Review of 8.01L
Prof. Min Chen
9/27/2015
Super-full Moon eclipse tonight at 11pm
Mid-Autumn Festival

Extra problems

Given v find a