Answer:
Explanation:
Given:
dimension of uniform plate,
mass of plate,
Now we find the moment of inertia about the center of mass of the rectangular plate is given as:
where:
length of the plate
breadth of the plate
We know that the center of mass of the rectangular plane is at its geometric center which is parallel to the desired axis XX' .
Now we find the distance between the center of mass and the corner:
Now using parallel axis theorem:
Answer:
6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
Explanation:
What matters is the part , the other parts of the equation don't affect time and space variations. We know that when the sign is - the wave propagates to the positive direction while when the sign is + the wave propagates to the negative direction, but <em>here is an explanation</em> of this:
For both cases, + and -, after a certain time (
), the displacement <em>y</em> of the wave will be determined by the
term. For simplicity, if we imagine we are looking at the origin (x=0), this will be simply
.
To know which side, right or left of the origin, would go through the origin after a time (and thus know the direction of propagation) we have to see how we can achieve that same displacement <em>y</em> not by a time variation but by a space variation
(we would be looking where in space is what we would have in the future in time). The term would be then
, which at the origin is
. This would mean that, when the original equation has
, we must have that
for
to be equal to
, and when the original equation has
, we must have that
for
to be equal to
<em>Note that their values don't matter, although they are a very small variation (we have to be careful since all this is inside a sin function), what matters is if they are positive or negative and as such what is possible or not .</em>
<em />
In conclusion, when , the part of the wave on the positive side (
) is the one that will go through the origin, so the wave is going in the negative direction, and viceversa.