# Lecture 1 - Motion, in 2 columns for easy printing+reading, includes diagrams I drew on the computer

by OC3700

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Motion

Types:

Translational – straight line

Circular – circular path, turning

Projectile aka Free-fall– following a curved path, the

only force on the object is gravity

The Particle Model

-Restrict attention to objects in motion

-Consider moving object as if a single point

without size or shape, no distinction btwn top +

bottom or front + back

-Treat as if all mass were concentrated into a

single point this object is a particle

Motion Diagrams

Basically overlaying all frames of a movie strip on

top of each other

Of an object at several instants in time

More space btwn dots = moving faster

Faster velocity = longer vector line

Mention Start/Stop if they are there

Vector Addition

Vectors = made up 2#s (magnitude +

direction/angle), always straight

ex. Force

C = A+B

Methods: tip-to-tail, parallelogram, components

(using x-y axis, can add on calculator )

Tip-to-tail:

oDraw A

oPlace B tail @ A tip

oDraw arrow from A tail to B t ip

This is vector A + B = C

Vector Subtraction

D = A – B = A + (-B)

-B is a vector with the same slope of B, but with

the tail and tip switched

ex. If B = , - B =

Tip-to-tail:

oDraw A

oPlace –B tail @ A tip

oDraw arrow from A tail to –B tip

This is vector A – B = D

Distance (scalar): d, path length [m]

Displacement (vector): ∆r, final position (r

f

) – initial

position (r

i

) [m, direction/angle]

d ≥ |∆r|

|x| = magnitude of vector x

Instantaneous velocity aka velocity (very small ∆r):

Vector v = lim

∆t

0

(∆r/∆t) = dr/dt [m/s]

Vector v

avg

= r

1

- r

0

= ∆r [m/s]

∆t ∆t

Linear Acceleration:

vector a

change in velocity (vector) not speed ( |v|, scalar)

over time

velocity can change in magnitude + directio n

find vector a by drawing ∆v

odo this by drawing v

n+1

– v

n

= v

n+1

+ (-v

n

)

odirection of ∆v = direction of a

odraw vector a at the midpoint of v

n

and v

n+1

(

a = avg a at this midpoint)

Vector a = lim

∆t

0

(∆v/∆t) = dv/dt [m/s

2

]

Vector a

avg

= v

1

- v

0

= ∆v [m/s

2

]

∆t ∆t

Signs

Position (x, y): sign tells where the object is

+r : to the right or above the origin (like

in a co-ordinate axis)

- r : to the lef t or below the origin

Velocity (v

x

, v

y

): sign tells what direction the object is

moving in

+v : moving upwards or to the right

- v : movin g downwards or to the left

Acceleration (a

x

, a

y

): sign tells the direction of the

acceleration vector, does not tell if speeding up or

slowing down

+a : a vector points up or right; can be

when v speeding up, or

when v but slowing down

- a : a vector points down or left; can

be when v but slowing down, or

when v speeding up

Iff (if and only if):

a vector direction = v vector direction: speeding

up

a and v vectors are in opposite directions:

slowing down

a vector = 0: velocity constant

Note: Centripetal acceleration occurs when when

turning at the same speed (changing velocity direction)

www.notesolution.com

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