14
votes
Accepted
Energy Conservation in electromagnetism
we can also express everything I've said about magnetic field too
Here is your mistake. In fact, in the situation you have described the magnetic fields must add constructively.
Recall that for an EM ...
- 81.9k
7
votes
Exact statement of conservation of momentum
Wikipedia's "in a closed system" and Taylor's "if there are no external forces on a pair of particles" are the same assumption, when applied to a pair of particles. In particular, ...
- 42.3k
2
votes
Problem with two dimensional collision
Hint: $\vec p = \sum \vec p_i = const. $
Ok, assuming:
this really is no homework
you know that r, v, p and M all are vector quantities
$E_{kin}$ is a scalar from a scalar product $\sum \frac{1}{m_i}...
- 404
2
votes
Accepted
Is the divergence of the energy tensor related to the equations of motion?
The conservation of the energy-momentum tensor is indeed related to the equation of motion in the sense that it is only conserved if the equations of motion are satisfied. One way to see this is the ...
- 587
1
vote
Why does expanding gas not cause thrust/opposite momentum?
While your thinking has some mistakes in it, you are on the right track overall.
The expanding gas does press on all surfaces with the same pressure. The force on the back of the cannon is the same as ...
- 31.1k
1
vote
Accepted
Can we say the momentum of a system is always equal to the momentum of the components of the system?
Velocity of the system is better translated as velocity of the centre of mass. We can use the definition of centre of mass: $$\mathbf R{cm} = \frac{M\mathbf R_M + m\mathbf R_m}{M+m}$$ Taking the ...
- 13.7k
1
vote
Accepted
In a rigid body rotating in 3D around the origin, is the norm of the linear velocity of each particle constant?
In general, you have the velocity field of solid body can be written at every time:
$$
v= v_0+\omega\times r
$$
with $v_0,\omega$ depending a priori with time. In particular, acceleration is:
$$
\dot ...
- 5,108
1
vote
Unclear negative sign in rocket propulsion equation
$m$ is the mass of the rocket and $dm$ is the change in the mass of the rocket after burning a small amount of fuel. The negative sign means that the rocket is losing mass. In other words, the initial ...
- 81.9k
1
vote
Accepted
Understanding Constants of Motion and the dimension of the effective Space available
Remember that you are interested in calculating trajectories. By definition, trajectories lie in CoM’s level sets. So when you have multiple CoM’s, trajectories lie in the intersection of their level ...
- 5,108
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