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Got a physics I problem I'd like some help with if anyone is up for helping a brother out. Just guidance is more than sufficient. It seems like a basic circular motion problem, but I missed the lecture on it when my professor taught it in class. Here's the problem:
The angular velocity of a process control motor is w = (20 - .5*t^2) rad/s, where t is in seconds.
a. What time does the motor reverse direction?
b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?
So here's my thought process on this one. For part a), set w (the angular velocity) to 0 to solve for t (where I'm guessing is the point that the motor changes direction). So
0 = 20 - .5*t^2 >> t = sqrt(40) s.
For part b), take the derivative of the equation to get the angular acceleration, plug it into
Af = Ao + wi*t + .5(alpha)*t^2 to get the answer in radians, then convert to degrees if I want to. I ended up getting -20.13 degrees for my final answer, or 125.49 rads.
This question doesn't exist on any website (trust me, I've tried looking) so there is no way I can check my answer (not in the back of my textbook). Any guidance AT ALL will be most appreciated!
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Confused about contour integration. I'm trying to integrate (x - sinx)/x^3 along the real axis. Should get pi/2.
Confusing me for two reasons. Firstly... the normal thing to do would be to consider the imaginary part of z + e^iz / z^3, where the contour goes along the real axis, dodging z = 0 with a semicircular arc, and then round the upper half plane in a big semicircle. But when I take the limit of the little semicircle, I get something like pi/r^2, which is unbounded as r goes to 0.
Also... I note that the integrand has a removable singularity at z = 0. So why can't I just like... remove the singularity. Then I've got an everywhere-analytic function... but then if I integrate along the real line and along a semicircle in the upper half plane, I should get 0, which is wrong.
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Check the boxes beside the statements that are TRUE, regarding force and motion.
Select all that are True.
1 If an object's speed does not change, no net force is acting on the object.
2 In order to not slow down, an object moving at a constant velocity needs a small net force applied.
3 If two different objects are under the influence of equal forces, they will have equal accelerations.
4 The net force acting on an object that maintains a constant velocity is zero.
5 The net force acting on an object that remains at rest is zero.
6 If a net force acts on an object, the object's velocity will change.
Review Newton's First and Second Laws and the definition of acceleration.
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How would i go about calculating the area of a circle, using integration?
Lets say the circle is x^2 + y^2 = r^2.
Of course we know that
I imagine there would be a way to describe an infinitely thin piece of a circle, such as the radius, and summ them all up.. or maybe describe an infinitely small segment and sum all segments.
This is bound to be super easy, but i can't figure it out.
I probably don't understand integration, or something.
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So, /sci/, a few hours ago, I responded to an obvious troll over on /vp/ (>>>/vp/11302870 I don't know how to cross post between boards) out of boredom regarding what the odds were of encountering two shiny Pokemon (for those of you who don't know or care enough to look it up: a Pokemon that uses an alternate color palate, they are very rare) of the same gender in a row; and given I was bored, I came up with a what I believe to be an equation to determine the odds:
>1:8192 are the basic odds of encountering a shiny Pokemon (technically 8:65536, but simplified to 1:8192); E stands for the number of encounters with shiny Pokemon in a row; G standing for the number the gender ratio of the gender in question must be multiplied by to produce 100; and R being the encounter rate percentage of the Pokemon in question divided by 100.
So, given that this IS the math board, I'm here to ask you guys: are there any glaring holes in my math that I'm blind to? And if there are, would anyone be willing to help me fix them?
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What does (dy/dx) actually mean? That is, I can perform algebra on this thing, but what am I really doing?
Note that I know that the "d" represents change, so it's describing infinitely small changes, but why can I perform these different manipulations to this thing?
Also, what's the difference between explicit and implicit differentiation? I know how to do this stuff, but I want to know why it works, and what it's saying.
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So if you use the newtonian gravity equation, during a solar eclipse, where the moon is directly between the earth and the sun, the gravitational force on the moon by the sun is about twice as great as earth's on the moon, at the same time the moon's velocity is basically tangential to its orbit around earth, so it's not like it's moving towards earth which could serve to work in earth's "favour". A simple inspection would lead you to the conclusion the moon should start to orbit the sun, but why does it not? Seriously im a pleb, and dont know.
Is it that if you account for earth's velocity with respect to the sun, or something, I really dont know, please respond