4.vježbe

h

O

b

y

C

b v vj A v v¢

v v

x

h

b 2

r z

v vr

b

C

h

v vJ

J

v r

J O

v v¢

A

A¢

C¢

h

dv dx d d Þ vII = = 4×t Þ a IIt = II = 4 cm/s 2 = konst. dt dt dt dt ------------------------------------------------------------------------------------------------------------x = 4 + 2×t2

Za t = 2 s :

vII = 8 cm/s

a1 =

a IIt r2

a IIIn =

vIII r3

Þ

Þ

w1 =

v II r2

Þ

a It = a 1 × r1 = a IIt

vI = w1 × r1 = vIII

v

w k

Brzina točke E: v

v

v

w = -w × sin a × j + w × cos a × k sin a =

10 10 2 + 12 2

cos a =

,

12 10 2 + 12 2

v v v rE = r × i - k × j --------------------------------------------------------------------------v i

v j

v k

r

-k

0

v v v v v v vE = w ´ rE = 0 - w × sin a w × cos a = v x × i + v y × j + v z × k

vE = v x2 + v 2y + v z2

Ubrzanje točke E:

v i v v v v v a E = a ´ rE + w ´ vE = 0 vx 0 a E = a x2 + a y2 + a z2

v v j k v v v - w × sin a w × cos a = a x × i + a y × j + a z × k vy vz

v rE

an

a = at2 + a n2 = 2

Þ

4 = at2 + an2

at = a × r

v2 r ------------------------------------------------------------------------an =

æ v2 4 = (a × r ) + çç è r 2

ö ÷÷ ø

2

Þ

v

-------------------------------------------------------------------------

at =

dv dt

Þ

a = konst.

Þ

t=

v at

at

v vx v v

vx v Þ v= x v sin j -----------------------------------------------------------------sin j =

v v v v =w´r

Þ

w=

v r

j