Recent content by wrobel

https://en.wikipedia.org/wiki/Statically_indeterminate

In order for simplicity sake some authors make the narration harder. By definition the kinetic energy of a particle is ##T=\frac{m}{2}|\boldsymbol {\dot r}|^2=\frac{m}{2}(\boldsymbol {\dot r},\boldsymbol {\dot r}).## Thus we have ##\dot T=m(\boldsymbol {\dot r},\boldsymbol {\ddot...

The point of JimWhoKnew can be illustrated by the following simple analogy. Consider an initial value problem ##\dot x^2+x^2=1,\quad x(0)=0,\quad t\ge 0.## It has a solution ##x(t)=\sin t## for all ##t\ge 0##; and another solution ##x(t)=\sin t## for ##t\in[0,\pi/2]## and ##x(t)=1## for...

Bring the proofs please.

The point P is a point of the lab system that coincides with the end of the rod before the collision. If the collision happens at the moment ##t## then the angular momenta of the system about P at the time ##t-0## and time ##t+0## are the same. A complete system of equations for the...

I do not know what OP means. I do not see equations of motion for the system of 3 degrees of freedom and I do not see a derivation of formula (7)

In #1 the rod AB is fixed relative the lab frame. The system has 2 degrees of freedom. I suggested a system with 3 degrees of freedom.

It is interesting to answer the same question assuming that the rod AB can rotate freely about the vertical axis

The original statement of the problem is that the rod AB can not rotate so there must be a torque that keeps it at rest. I don't see any ambiguities in the original statement.

If the rod AB can rotate freely about the vertical axis then the projection of the angular momentum of the whole system on the vertical axis is conserved. Another task is calculate this projection correctly

I do not think that the angular momentum of the whole system about the vertical axis is conserved because of this:

In science fiction movies (Interstellar for example) people organize a rotation of a spacecraft to provide an artificial gravity by means of a centrifugal force. Besides the centrifugal force there is a Coriolis force as well. This force influences the blood flow in vessels for example. Can it...

Old thread but it dives up as a hot thread every time . I just want to say that there are several definitions of arc length. Math begins from definitions.

It is interesting to think about ##k\to\infty##