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Mechanics

Hot goIITian

Joined:	25 Feb 2008
Post:	177

29 Mar 2008 19:35:16 IST

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307

and how do you solve this??

None

A rigid body is rotating at 5 rad/s about an axis through origin and with direction cosines 0.4, 0.6 and 0.8 with respect to x, y and z-axis respectively. What is the magnitude of velocity of a point in the body defined by the position vector r = ? 2i + 3j ? 4k with respect to the origin.
(a)
(b)
(c)
(d) None of these
Ans5 (c)

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Akhil

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29 Mar 2008 19:38:37 IST

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v=w x r

here w=(0.4 i + 0.6 j+ 0.8 k)5
r=2i+3j+4k

are the question marks - signs or plus signs?

SRM

Hot goIITian

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29 Mar 2008 19:44:42 IST

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minus signs...

SRM

Hot goIITian

Joined: 25 Feb 2008

Posts: 177

29 Mar 2008 19:48:00 IST

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i don't get it????

Akhil

Blazing goIITian

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29 Mar 2008 19:48:07 IST

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then |v|=|r x v|
=|(2i+3j+4k)x(-2i+3j-4k)|
=|-24 i +12 k|
=12|-2i+k|
=12root(2^2+1)
=12root 5

BALGANESH

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29 Mar 2008 19:51:55 IST

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akhil
direction cosines means the value cos @ , where @ is the angle between w and the axis

is it ...
if not explain plz

Akhil

Blazing goIITian

Joined: 17 Jan 2008

Posts: 1451

29 Mar 2008 19:54:36 IST

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it does...
so with x axis if it makes angle cos inverse (0.4)
it is a unit vector, projection of 0.4i on x axis=0.4=cos @
so the vector can be written as
0.4 i +0.6 j+0.8 k
and magnitude=5
so w=5(0.4i+0.6j+0.8k)
=2i+3j+4k

correct me if wrong

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