i have nothing against george tsiros though he insulted me he praised me before
different size marbles fall at same rate down a ramp, i discussed it before maybe this convinces you:
quote:
Originally posted by raaaid:
same mass, half rotational speed, cuadruple moment of inertia implies double rotational energy
so the same mass but with double radius ends with same linear energy but double rotatioanl energy
Wrong. "same mass, half rotational speed, cuadruple moment of inertia implies double rotational energy" No, it does not and I don't know where you got this from. It does not have quadruple moment of inertia, only double, since angular velocity is only half the original and moment of inertia is quadruple.
Let's calculate it. So, we have two spheres, first one m=1 (kg), r=1 (m), second one m=1 (kg), r=2 (m). Moment of inertia for a sphere is I=(2mr^2)/5.
First one rotates at an angular velocity omega, second one at omega/2, right? Then, rotational kinetic energy of the first sphere is:
Wkr1=(I*Omega^2)/2=([(2mr^2)/5]*Omega^2)/2=
m*r^2*Omega^2/5.
Now, for the second sphere:
Wkr2=(I*(Omega/2)^2)/2=([(2m
(2r)^2) /5]*(Omega/2)^2)/2=
m*r^2*Omega^2/5.
Look, what a coincidence! They are the same!!
What you are forgetting here raaaid is, that a double sphere will have QUADRUPLE moment of inertia, not double.
Now let's calculate it AGAIN, this time using moments of inertia
:
First sphere will have angular momentum:
Gama1=I1*Omega1=((2mr^2)/5)*(v/r)=(2mrv)/5 since I=(2mr^2)/5 and Omega=v/r.
and, since Wkr=(I*Omega^2)/2 and Gama=I*Omega, we can derive
Wkr=Gama^2/(2*I)=(2mrv)^2/(5^2*(2mr^2)/5) =>
Wkr1=(2mv^2)/5
Second sphere will have angular momentum:
Gama2=I2*Omega2=((2m((2r)^2))/5)*(v/2r)=((2m((2r)^2))/5)*(v/2r)= (4mrv)/5
from which we derive rotational kinetic energy same way as above, Wkr=Gama^2/(2*I)
So, Wkr2=Gama2^2/(2*I2)=[(4mrv)/5]^2/[(2*m(2r)^2)/5]=, believe or not, exactly the same as for the first sphere:=>
Wkr2=(2mv^2)/5.
Again, half the rotational velocity with double the radius
does not imply quadruple angular momentum, only double, since it is the product of angular velocity (which is halved) and moment of inertia (which is quadrupled).
All clear now?
from here:
http://forums.ubi.com/eve/foru ... 23110283/m/9821018375/p/4
in fact what i say is:
current physics state that different sizes marbles will fall down a ramp at the same rate and this was exactly galileo experiment
i tested it myself and i could check than he bigger one fell 1st
this was due to george inviting me to test physics by myself just as galileo, so i told him i had done galileo experiment with different results
i dont think this is bull sheet, bigger marbles fall down a ramp faster than smaller ramp, this contradics current physics and anybody can test it
now will you care to check if you are being lied as i did, or youll just think that theres no the slightest mistake in basic physics, that when most agree it must be true
im sorry to say that is obvious in the other forum there are more helpfull people