Hi friends
suppose there a circular disc of radious R, rotating about its axes at the center. the relationship between angular velocity and linear velocity is given by
There is a formula V=ω x R (cross product)
where V-linear acceleration
ω- angular velocity
R-Radious
This expression shows that ω and R are perpendicular, and V is perpendiculat to both ω and R.
why there are expressing V as ωxR, why not Rxω ??????
as we know axb≠bxa.
On what assumption we are denoting ω in the first and R as second term ?
simillarly
angular momentum L=R x P
=Rx mv
P-linear momentum
L-angular momentum
I agree with mrflibble, it is just convention. I would recommend you to stay with that (to avoid minus signs).
You have similar thing with the Poynting vector:
S = E х H.
If you change E with H, S doesn't point in the direction of energy flow (given used definitions of E and H).
In your case, when omega points in positive Z direction, the disc rotates counter clockwise when you look at the xy plane (z points towards you). If you make a picture when the red dot on the rotating disc is at the x axis, v has an y-component only. This follows also from
v =ω x R
(as you noted already)
for imagination of the cross product: I use
X x Y = Z (all unit vectors, Z pointing towards you).
As you already noted, interchanging x and y will result in -Z.
As you can decompose any vector in its XYZ components, you can apply this to every orientation. If problems, make yourself a three dimensional model from metal wire.
We typically work in a right handed system....defined by i cross j equals k....{i,j,k} being the basis vectors (or a set of basis vectors)...to convince yours elf that this is consistent draw a diagram...a point on the x axis say at x=r...rotate that point about the z axis in the xy plane with angular frequency w....consider the angular rotation represented by the vector W = w*k (k the unit vector in the plus z direction)...now look at the motion with algebra and vectors using the cross product...
The first step is almost always to draw a diagram that represents the system...
hi friends
Thank for your suggesions......
By referring some websites documents presented, it was found that. The assumption made is based on the Right handed rule(with curling fingers). These following we links giving some clear picture on how to make assumptions. It was really helpfull...
Hi friends
suppose there a circular disc of radious R, rotating about its axes at the center. the relationship between angular velocity and linear velocity is given by
There is a formula V=ω x R (cross product)
where V-linear acceleration
ω- angular velocity
R-Radious
This expression shows that ω and R are perpendicular, and V is perpendiculat to both ω and R.
why there are expressing V as ωxR, why not Rxω ??????
as we know axb≠bxa.
On what assumption we are denoting ω in the first and R as second term ?
simillarly
angular momentum L=R x P
=Rx mv
P-linear momentum
L-angular momentum