I'm sorry if I'm being unclear, I'm sick and tired so I'm a bit foggy. Let me try to lay out what I meant more clearly.
We often model very small quantities as being infinitesimal even though they aren't necessarily actually infinitesimal, so far as we can tell. For instance, we can model very...
In K&K's Intro to Mechanics, they kick off the topic of rotation by trying to turn rotations into vector quantities in analogy with position vectors. It's quickly shown, however, that rotations do not commute, making them rather poor vectors. They then show, however, that infinitesimal rotations...
For a damped mechanical oscillator, the energy of the system is given by $$E = \frac{1}{2}m \dot{x}^2 + \frac{1}{2}k x^2$$ where ##k## is the spring constant. From there, I've seen it dictated that the average kinetic energy ##\langle T \rangle ## is half of the total energy of the system. This...
If I'm given a function ##f(x) = A cos (x) + B sin (x)##, is there any way to turn this into an expression of the form ##F(x) = C e^{i(x + \phi)}##? I know how to use Euler's formula to turn this into ## \alpha e^{i(x + \phi)} + \beta e^{-i(x + \phi)}##, but is there a way to incorporate the...
I imagine he's referring to the "numerator" of a second derivative such as ##\frac{d^2 \vec{r}}{dt^2}## in analogy with his identification of the differential form ##d\vec{r}## with the "numerator" of a first derivative.
I've had three courses on introductory mechanics, the first from an algebra based text called Physics of Everyday Phenomena by Griffith, the second from a calculus based book called Fundamentals of Physics by Halliday (my first courses in E&M, thermal physics, and optics also came from this...
And you understand right, correct? The average acceleration of the car is ##5 \frac{m}{s^2}##, and multiplying that by the time given (ten seconds) gives you the velocity at that time.
So the system we're considering is the two objects, right? In this case, the gravity between these two objects is an internal force because it only involves objects in our system.
Now imagine a different situation: we still have our two objects, and they're in our system, but there's also a...
Momentum is always conserved when no external forces are acting on the system. So as long as your system is the two objects, and no other objects are interacting with them, then yes, momentum is conserved.
Kinetic energy is not, in general, conserved, but the total energy is.
In non-relativistic mechanics, we learn that momentum is given by ##p = mv##, but in relativity it comes out that the relationship is actually $$E^2 = (pc)^2 + (mc^2)^2$$ where ##c## is the speed of light and ##E## is the energy. For a photon, ##m = 0##, which gives us $$E = pc$$ And we know...
Light possesses momentum, so in that sense it can certainly move matter in the form of radiation pressure. Was there anything in particular you were looking for?