Class 2: Displacement and velocity Metric system Units can be - - PowerPoint PPT Presentation

▶

Aug 24, 2022 300 likes •403 views

Class 2: Displacement and velocity Metric system Units can be modified by a prefix. Common prefixes: e.g. millimeter = 10 -3 m m (milli) = 10 -3 e.g. microgram = 10 -6 g (micro) = 10 -6 e.g. nanometer = 10 -9 m n (nano) = 10 -9 e.g.

SLIDE 1

Class 2: Displacement and velocity

SLIDE 2

Metric system

Units can be modified by a prefix. Common prefixes: m (milli) = ×10-3 e.g. millimeter = 10-3 m  (micro) = ×10-6 e.g. microgram = 10-6 g n (nano) = ×10-9 e.g. nanometer = 10-9 m p (pico) = ×10-12 e.g. picosecond = 10-12 s K (kilo) = ×103 e.g. kilogram = 103 g M (Mega) = ×106 e.g. Megaton = 106 ton G (Giga) = ×109 e.g. Gigabyte = 109 byte T (Tetra) = ×1012 Note: SI units of mass is kg, or kilogram, equals to 103 g. Gram (g) is not an SI units. Sean Mauch -- Should be Tera

SLIDE 3

Coordinates (1D)

1m 2m

3m 4m 5m

1m 2m

3m 4m 5m

xf = +4m xf = -3m xi = +3m xi = -2m It is important to define the direction and origin (0) of the axis which the coordinate refers to. i f

SLIDE 4

1m 2m

3m 4m 5m

i f

Displacement x (1D)

1m 2m

3m 4m 5m

xf = +4m xf = -3m xi = +3m xi = -2m x= xf - xi = +4-(-2) = +6m x= xf - xi = -3-(3) = -6m

SLIDE 5

xi = +3m xf = -3m xi = +3m xf = -3m 1m 2m

3m 4m 5m

i f

Displacement x and distance d (1D)

1m 2m

3m 4m 5m

xf = +4m xi = -2m x= xf - xi = +4-(-2) = +6m x= xf - xi = -3-(3) = -6m d = 6m d = 6m d = |x| if there is no U-turn 1m 2m

3m 4m 5m

i f 1m 2m

3m 4m 5m

xf = +4m xi = -2m x= xf - xi = +4-(-2) = +6m x= xf - xi = -3-(3) = -6m d = 8m d = 8m d  |x| if there is U-turn

SLIDE 6

xf = -3m xi = +3m 1m 2m

3m 4m 5m

Average velocity and average speed (1D)

1m 2m

3m 4m 5m

xf = +4m xi = -2m x= xf - xi = +4-(-2) = +6m x= xf - xi = -3-(3) = -6m d = 8m d = 8m at ti at tf

t d t t d speed Average t x t t x x velovcity Average

i f i f i f

         

Average speed = |average velocity| if there is no U‐turn Average speed  |average velocity| if there is U‐turn

SLIDE 7

Instantaneous velocity and Instantaneous speed (1D)

t d Lim speed Average Lim dt dx t x Lim velovcity Average Lim v

t t t t x

        

       

Instantaneous velocity Instantaneous speed

1. In mechanics, only instantaneous velocity and speed are important.

Average velocity and speed are just introduced to define their instantaneous

values. So from now on, by velocity or speed, we mean instantaneous velocity

and instantaneous speed.

2. When t  0, no U‐turn is possible. So

instantaneous speed = |instantaneous velocity|

always. For this reason, we will just write speed as |vx|. The absolute sign is

now called magnitude, speed is the magnitude of velocity (note I am beginning to drop the adjective instantaneous).

SLIDE 8

x‐t graph

x (position)

curve

slope dt dx vx  

U-turning. Stop instantaneously. U-turning. Stop instantaneously. Moving in the negative axis direction t (time) Moving in the positive axis direction

SLIDE 9

Preparation for next class

Read 2.4

dx dv v t d x d a

2 2 x

 

Eq. (2.12)

Not in text, but that doesn’t mean it is not important Try to convince yourself displacement x, velocity dx/dt, and acceleration d2x/dt2 are independent of each other – you can not tell one from the

ther. They can have different signs (8 possible combinations), practice

and think how the motion looks like for some of these combinations. For example, try to produce the motion with a pencil on a real number line if x is negative, v is positive, a is negative.