Unformatted text preview: Lecture 4: 09/15/11
note: text in red refers to the textbook, 9th edition extended.
1. Definitions of position, velocity and acceleration in 2D – sections 41 to 44
2. Unit vectors  sections 35 and 36
Unit vectors are just for mathematical convenience and help you write two equations (one for each
component) as one
3. Projectile motion – section 45
Projectile motion is the special case of motion in 2D where the acceleration is constant and has the form
⃗
̂
̂
The reason for the – sign is that by convention we assume that the direction of increasing y is pointing
away from the center of the earth
4. Projectile motion analyzed  section 46
5. Uniform circular motion – section 47
Uniform circular motion is the special case of motion in 2D where a particle moves with constant speed
around a circle. The position of a particle can be described as:
⃗⃗⃗⃗⃗⃗⃗⃗⃗
̂
̂
The magnitude of is R ( a constant) as can be checked by The velocity and acceleration can be obtained by taking derivatives of the position:
⃗⃗⃗⃗⃗⃗⃗⃗⃗
̂
̂
⃗⃗⃗⃗⃗⃗⃗⃗⃗
̂
̂
With their magnitudes similarly given by
⁄ ...
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This note was uploaded on 11/26/2011 for the course PHYISCS 1401 taught by Professor Dodd during the Spring '11 term at Columbia.
 Spring '11
 DODD

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