We started talking about speed during our very first week of class and we haven\
ID: 1410354 • Letter: W
Question
We started talking about speed during our very first week of class and we haven't ever stopped, though the context has shifted regularly. Here are a few: For each of those five formulas for speed identify: all the symbols that appear. What kind of speed this equation tells you, and for what kind of motion, (e.g. average, instantaneous, maximum, etc.) any restrictions or qualifications or other considerations necessary when using it (in other words, when can/can't this equation be used). This is an essay question, so give me full, meaningful sentences.Explanation / Answer
1) v = rw
v = instantaneous velocity
r = radius
w = radial velocity
B. instantaneous
C. When "properly" written, that equation you quote is
v = x r
where each of those three quantities is a vector. If you haven't dealt with vector algebra, and cross- and dot-products of vectors in particular, all you need to know is that the magnitude of both sides of that equation gives:
v = r sin
where v, , and r, are magnitudes of the above vectors, and so, are always non-negative.
And that is the angle between the vectors andr, and so is always between 0º and 180º inclusive, so that the sine is always non-negative.
Now the vector is defined in a way that will seem strange at first, but bear with me. If you picture whatever is turning, and you position the fingers of your right hand together in a 'curl,' with the thumb pointing out to the side, then just place your curled fingers so that they point in the direction of the rotation. Your thumb then points perpendicular to the plane of that rotation, in the direction of the vector. For circular motion, that will be always perpendicular to the radius vector,r, whenr is taken with the center of rotation as its origin. And in that case, is always ½, and sin=1.
And that's where
v = r
comes from.
2) v = at
V= Final Velocity
a = acceleration
t = time
B. Final velocity
C. You would use this if you wanted to find the final speed of a car after accelerating for t seconds or something
3) v = A
v = Maximum Velocity in SHM
A = Amplitude
= Angular Speed
B. Maximum Velocity in SHM
C. vmax occurs at the middle (x = 0) as the oscillating object passes the equilibrium position.
4) v = f Wave Equation
v = wave velocity
= wavelength
f = frequency
B) Wave velocity
C) a wave is produced when a vibrating source periodically disturbs the first particle of a medium. This creates a wave pattern that begins to travel along the medium from particle to particle. The frequency at which each individual particle vibrates is equal to the frequency at which the source vibrates. Similarly, the period of vibration of each individual particle in the medium is equal to the period of vibration of the source. In one period, the source is able to displace the first particle upwards from rest, back to rest, downwards from rest, and finally back to rest. This complete back-and-forth movement constitutes one complete wave cycle.
5) v = sqrt(r/mu)
v = orbital velocity
r = radius
mu = GM, is the standard gravitational parameter.
B) Orbital Velocity
C) The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. It can be used to refer to either the mean orbital speed, i.e. the average speed as it completes an orbit, or the speed at a particular point in its orbit such as perihelia.
The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy.
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