Dynamics - Classical Mechanics - Lecture Slides, Slides of Classical Mechanics

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Dynamics

Kinematic

Vectors

-^

Kinematic

quantities

refer

to

the

motion

only.

-^

Position

-^

Velocity

-^

Acceleration

-^

Kinematic

vectors

of

velocity

and

acceleration

are

coplanar.

dx^ dt x v^

i

i i^

^

rd dt r v

^ 

^

^

r v a^

^

i i i^

x v a^

^

x^2

 r^2  r^1

 v^1

 a^1  v^2

 a^2

x^1 Docsity.com

Forces

on

One

Particle

-^

There

is

a^

net

force

on

each

particle

in

an

object.

-^

This

corresponds

to

the

particle’s

acceleration.

2 2

2 2

)

(^ dt

r m d

dt

r d m a m F

       





^







m^    r

Forces

on

a

System

-^

For

N

particles

in

a^

system

the

forces

add.

-^

Particles

of

constant

mass

-^

Some

forces

are

internal

and

some

are

external

to

the

system.^ –

Internal

forces

cancel





N

N

total

dt

r m d

F

F^

1

2 2

1









m^ 

 r 

)(  ^ FINT

)(   FEXT













N

N

INT

N

EXT

total

dt

r m d

F

F

F^

1

2 2

1

)(

1

)(

) ( 



















  FINT









N

N

net^

r m

M d dt M

dt

r m d

M M

F^

1

2 2

1

2 2

1

) (















N  

m

M

(^1) 



Docsity.com

Sliding

Inclined

Plane

 F^1

gm

F^

bg

^

(

-^

The

block

and

inclined

plane

are

both

free

to

move.

-^

Two

frictionless

surfaces

-^

The

coordinates

should

point

along

the

surface.

-^

Normal

force

is

the

force

of

constraint

-^

The

motion

will

be

along

the

surface

-^

Acceleration

from

plane

and

block

relative

to

plane



cos mg

sin mg

ˆ i

M

1 )(

)

(^

F

F

a A m^

bg

^



^

sin

cos

mg

ma

mA



^

cos

sin

1

mg F

mA

Motion

of

Plane

 F^2

g M

F^

pg



^

) (

-^

The

inclined

plane

has

two

forces

from

constraints.

-^

Upward

from

table

-^

Reaction

from

block

-^

The

system

of

linear

equations

are

solved

for

the

accelerations.

^

ˆ i

M

1 2 )(

F

F

F

A

M

bg

^

 sin 1 F

MA

 cos

1 2

F

F

Mg

 F^1 





^

cos

sin

1

mg F

mA



^

sin

cos

mg

ma

mA

m M

g

A^



  2 sin

cos sin

^

m M

g a





^

2

2

sin

cos

1

sin