8/9/2019 LEC 23 (Planar Kinematics 051)

1/19

King Fahd University of Petroleum &Minerals

Mechanical Engineering

Dynamics ME 201

B

Dr! Meyassar "! #l$%addad

ecture ' 2(

8/9/2019 LEC 23 (Planar Kinematics 051)

2/19

)ourse coverage

Kinematics of particle in various motion. (Chapter 12)

Force and acceleration. (Chapter 13)

Work and ener! relations. (Chapter 1")

#mpulse and $omentum. (Chapter 1%)

Kinematics of a riid &odies. (Chapter 1')

Force and acceleration of a riid &odies . (Chapter 1)

Work and ener! relations of a riid &odies. (Chapter 1)

#mpulse and $omentum of a riid &odies (Chapter 1*)

8/9/2019 LEC 23 (Planar Kinematics 051)

3/19

Chapter 1' +lanar Kinematics of a ,iid -od!

&/ective

0o classif! the various t!pes of riid&od!.

0o investiate riid&od! translation and

sho ho to anal!e motion a&out a fi4ed

a4is.

8/9/2019 LEC 23 (Planar Kinematics 051)

4/19

,iid-od! $otion

0!pes of riid &od! planar motion5

0ranslation

,otational a&out fi4ed a4is

6eneral plane motion

8/9/2019 LEC 23 (Planar Kinematics 051)

5/19

0ranslation

7ver! line sement on the &od! remains parallel to its oriinal direction

durin the motion

8/9/2019 LEC 23 (Planar Kinematics 051)

6/19

,otation a&out fi4ed a4is

8ll particles of the &od! move alon circular paths

e4cept those hich lie on the a4is of rotation

8/9/2019 LEC 23 (Planar Kinematics 051)

7/19

6eneral plane motion

Com&ination of translation and rotation

8/9/2019 LEC 23 (Planar Kinematics 051)

8/19

74ample

,ectilinear translation ,otation a&out a fi4ed a4is

Curvilinear translation6eneral plane motion

8/9/2019 LEC 23 (Planar Kinematics 051)

9/19

0ranslation

ABAB /rrr +=

+osition

AB

AB

ABAB

const

dtd

vv

.r

/rvv

/

/

=

=

+=9elocit!

8cceleration

AB aa =

8ll points move ith same velocit! and acceleration

8/9/2019 LEC 23 (Planar Kinematics 051)

10/19

:ummar! chapter 12 0ime dependent acceleration

dt

dsv =

)(ts

2

2

dt

sd

dt

dva ==

dvvdsa =

Constant acceleration

tavvc

+=0

2

002

1tatvss

c++=

)(2 0202 ssavv c +=

8/9/2019 LEC 23 (Planar Kinematics 051)

11/19

,otation 8&out a Fi4ed a4is

For ;ine

8nular +osition ( )

8/9/2019 LEC 23 (Planar Kinematics 051)

12/19

==dt

d

8nular velocit! ( )?the time rate of chane in the anular position@

==dt

d

8nular acceleration

?the time rate of chane of the anular velocit!@

==2

2

dt

d

> f()

dd =

8/9/2019 LEC 23 (Planar Kinematics 051)

13/19

Constant 8nular 8cceleration

)(2 0202 += c

tc

+= 0

2

002

1tt

c ++=

8/9/2019 LEC 23 (Planar Kinematics 051)

14/19

Comparison

)(2

2

1

0

2

0

2

2

00

0

+=

++=

+=

c

c

c

tt

t

dt

dsv =)(ts

2

2

dt

sd

dt

dva ==

dvvdsa =

tavvc

+= 0

2

002

1tatvss

c++=

)(2 02

0

2ssavv

c

+=

dt

d=

2

2

dt

d

dt

d ==

dd =

)(t

8/9/2019 LEC 23 (Planar Kinematics 051)

15/19

8/9/2019 LEC 23 (Planar Kinematics 051)

16/19

8cceleration

ta

dt

d= ( )r

dt

d=

dt

dr

= r=

ran

2

= r

r 2)(

= r

2

=

8/9/2019 LEC 23 (Planar Kinematics 051)

17/19

2211 rrS ==

2211 rr ==

2211 rra ==

r1 r2

s B vB a

r1

r2

8/9/2019 LEC 23 (Planar Kinematics 051)

18/19

74ample 1'1

,est

at> "t ms2

>D

>D

ratP =)(

2/20

)2.0()4(

sradt

t

=

=

tdt

d20==

sradt

dttd

t

/10

20

2

0 0

=

=

210 tdt

d==

radt

dttd

t

3

0 0

2

33.3

10

=

=

8/9/2019 LEC 23 (Planar Kinematics 051)

19/19