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1d
comment Gravitation - hole to center of Earth
I don't know of another analytic one. You could certainly simulate it numerically.
2d
comment Gravitation - hole to center of Earth
You are solving a second order differential equation. It ise one of a harmonic oscillator: $\frac {d^2r}{dt^2}=-\frac {gr}R$. You get solutions in sine and cosine, but you will arrive at the surface with escape velocity and never turn around. This will come in with the constants of integration, which capture the initial conditions.
2d
answered Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?
2d
comment Gravitation - hole to center of Earth
I changed to $r$. It is the second time derivative.
2d
answered Gravitation - hole to center of Earth
2d
comment Gravitation - hole to center of Earth
@Gowtham: In fact, ignoring friction, it will escape to infinity after going out the other end. While inside the earth he equation is the same. We just have a strange initial condition.
Dec
16
answered Question regarding frequency of pendulum while it is stopping
Dec
15
comment Is it possible to use a magnet to move a steel carriage, which is tied to the magnet?
Please describe the setup in more detail. Is there an external force on the system somehow or are the carriage and magnet isolated from the rest of the world?
Dec
15
comment Is it possible to use a magnet to move a steel carriage, which is tied to the magnet?
@Hypnosifl: That could be the question, and you are right.
Dec
15
answered Is it possible to use a magnet to move a steel carriage, which is tied to the magnet?
Dec
14
answered What does a hot, optically thin gas *look* like?
Dec
14
comment How can we be Certain that Dark Matter Exists if we Cannot See it or Directly Detect It?
Have you read Wikipedia ? There is a long section on the observational evidence.
Dec
13
answered My python trajectory calculator for a small mass in a gravitational field - why is energy conservation violated?
Dec
13
comment What's the physical interpretation of an arbitrary normal mode for masses and springs?
Yes, the common frequency is where the eigenstuff comes from. You assume that each mass moves with a common frequency, but its own amplitude and phase. Then $\ddot x_i= \omega^2 x_i$ , you get $(A-\omega^2)\vec{x}=0$ and you want nontrivial solutions.
Dec
13
answered What's the physical interpretation of an arbitrary normal mode for masses and springs?
Dec
13
answered Why is the relationship between velocity and radius curved, in circular motion?
Dec
12
answered Does a bungee cord have a moment of inertia?
Dec
12
answered Computing lengths for a rotating rod
Dec
8
answered Copper Bath Keeping the Water Warm
Dec
6
comment How Earth's Gravity is more powerful than its centrifugal force?
This line of reasoning allows the earth to spin more slowly (reducing the centrifugal force to near zero) but sets an upper limit to how fast it can spin. What would be the length of a day if the centrifugal force at the equator equaled $g$? In that case, if you ran East, you would launch into orbit.