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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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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
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hey /sci/ I am having trouble with math, math is a weak subject of mine, but I would like to get better at it, and do very well with it. I am currently in college at the lowest math class they have. I am working with prime factorization, and Least common multiple. I would like to know what methods you use to solve in these two categories,
Least common multiple I am just confused, does it mean the smallest number that both of t hem go into.
so, lets says, numbers are 2 and 5, do I just find which answers will be the same from both of them? like 5 * 4 = 20 and 10 * 2 = 20 and so one of the LCM is 20?
is that even a efficient way or is there better/efficient way?
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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.