Motion of a Lamina - Mathematics & Physics

[elle]

Hi,

I'm not sure if this mechanics question should be in the Maths forum or the physics forum Nevertheless, I apologise first if I have posted in the wrong area

I was wondering if anyone could help me with the following question.

A lamina moves in its own O(x,y) plane. At a certain instant the displacement from one of its points P to another point Q is (-5i+10j). If the velocity of P is (7i-2j) and the velocity of Q has 5 as its x component:

1) What is the angular velocity of the lamina?
2) What is the velocity of Q?

In my notes I have been given the following equation:

$$v_Q$$ = $$v_P$$ + $$\\omega\\$$ + $$\\vec{PQ}$$

I've got the information for velocity of P and the displacement but I'm not sure how to express the velocity of Q in vector format? And how to I find the angular velocity? Is it just rearranging the equation for omega?

Please help, thanks!

 

[benorin]

the givens are $$v_P=7i-2j,\vec{PQ}=-5i+10j$$ and of $$V_Q$$, we know only the x-component, which is 5, so $$V_Q=5i+yj$$ where y is unknown. I think you mean to put your equation as

$$v_Q=v_P+\omega +\vec{PQ}$$

so we have $$(5i+yj)=(7i-2j)+\omega+(-5i+10j)$$

EDIT: The angular velocity $$\omega$$ a vector: for it must be.

Are, in fact, $$v_Q,v_P$$ the velocities of Q and P?

 

[elle]

Oh yeah, sorry I'm terrible at using Latex Yep that's the equation I meant.

Erm in my notes it says that the vector $$\omega$$ is = theta (with a dot on the top) k i.e its a vector

Yer $$v_Q,v_P$$ are the velocities of Q and P.

 

[benorin]

I didn't get the 3-D part until just... well then:

So we should have

$$(5i+yj+zk)=(7i-2j)+\vec{\omega} +(-5i+10j)$$

where y and z are unknown. Still not enough. You need more equations. Dig.