let
df=∂f/∂x dx+∂f/∂y dy and ∂f/∂x=p,∂f/∂y=q
So we get
df=p dx+q dy
d(f−qy)=p dx−y dqand now, define g.
g=f−q y
dg = p dx - y dq
and then I faced problem.
∂g/∂x=p←←←←←←←←←←←←←←← book said like this because we can see g is a function of x and p so that chain rule makes ∂g/∂x=p
but I wrote...
A sphere is rolling inclined wall (θ radian).
and the momentum of that sphere is
L = 1/2 mv^2 + 1/5 mv^2 + mgx sin(θ) = 7/10 m v^2 + mgx sin(θ)
∂L/∂v = p
7/5 m v = p
but I can't understand why the factor of mv is 7/5.
p is the linear momentum of sphere.
which means the factor of mv must be...
http://www.utdallas.edu/~pervin/ENGR3300/Boaz.pdf
see page 493
he said that first variation of I is
δI = dI/dε * dε
http://www.colorado.edu/ASEN/asen5227_offline/slides/292-334.pdf
but this pdf said (see page 309) that first variation of I is
δI = dI/dε * ε
(y and I commute, α and ε...
what makes you think that i calculated at different axes, before and after are same axes, they are just fixed simple axes. i calculate angular momentum about the reference axis after collision
OK PLZ UNDERSTAND MY QUESTION
Problem - if ball collasped with stick hangs two heavy masses and moved like test.png, After collision angular momentum must be zero cause no external forces there. But collision makes stick get spin, at origin point of that system feel non zero angular momentum...
fig (b) has no pivot - it's a free laminar motion
i know no external force means conservation of angular momentum
and i understood fig (b) must be same angular momentum
but it's also true that my set of origin point(same line with F) makes zero angular momentum before percussion because r and...
center of the bat is at the origin → i know that makes the ball starts with non-zero angular momentum
i mean that if i set the origin point it same line with ball's movement, that makes the ball and bat get zero angular momentum - and after the collision, angular momentum of totaol system is...
look figure (b)
suppose that baseball deliver F through horizontal motion.
imagine that the O point of the system is same line of F (+x is F direction)
then before percussion, the angular momentum of the system is "0" because r and v of baseball are same direction (L = r x mv = 0)
so after...
the direction of angular momentum of that body is southeast direction.
and because of rotation, angular momentum rotates inward direction of page.
so, that means direction of torque(=chage of angular momentum) is clockwise.
but the wiki page said that the torque's direction is...
https://en.wikipedia.org/wiki/Balancing_of_rotating_masses
See the image in that page.
I know intuitively why a direction of torque is counterclockwise-because of a centrifugal force.
But an direction of angular momentum of that shaft with attached weights (ignore the shaft mass) is southeast...