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    Linear velocity of a rotating body

    Homework Statement A flat rigid body is rotating with angular velocity 3 rads-1 about an axis in the direction of the vector (i + 2 j + 3 k) and passing through the point (1, 1, 0) on the body. Find the linear velocity of the point P = (1, 0, 1) on the body. (You may use the result v =...
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    Applications of vector algebra to physics

    Homework Statement A ball of mass 1 kg is acted upon by three forces: Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N. Determine a vector expression for the acceleration of the particle. If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s...
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    Finding the mass of an atom - bainbridge mass spectrometer question

    Q. In a particular spectrometer, doubly ionised \stackrel{12}{6}C and singly ionised \stackrel{6}{3}Li atoms are detected. The ratio of the path radii is 1.00252, the Li having the larger value. The fields are constant. Find the mass of of the lithium atom. I can only think of the equation...
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    Fourier Transformation integral

    I'm trying to integrate a function which is given as F(u)= \int f(x)e^{-2}^{\pi} ^{i} ^{x} ^{u} dx with limits of +ve and -ve infinity integrating by parts gives me \frac{1}{2} f(x)^{2}e^{-2}^{\pi}^{i}^{x}^{u}-\frac{1}{2} \int f(x)^{2}xe^{-2}^{\pi}^{i}^{x}^{u}dx fisrt off, is the...
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    Differential Equation

    I'm trying to solve this firrst order diff. equation, where I'm given the initial value, x(0)=2 \frac{dx}{dt}=\frac{3x+4}{\sqrt{t}} \frac{dx}{3x+4}=\frac{1}{\sqrt{t}}dt \int\frac{1}{3x+4}dx=\int\frac{1}{\sqrt{t}}dt ln(3x+4)=ln(t^{\frac{1}{2}}) this is as far as I got, do I sub in x(0)=2...
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    Integration problem

    is \int\frac{dx}{1+x^{2}} the same as \int\frac{1}{1+x^{2}}dx ?
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    F=ma calculation in vector format

    I am given F=(3i + 2j + 4k) N and mass = 2kg I need to calculate acceleration, so I plugged it into F=ma, am I right in saying (3i + 2j + 4k) = 2 a \frac{(3i + 2j + 4k)}{2} = a therefore a = 1.5i + 1j + 2k ? cheers.
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    Writing an equation for a wave

    I needed to write an equation for a wave with: amplitude : 2cm wave vector : 502.7 angular frequency : 125.7 Hz time : 0 sec and I used the general equation for waves to come up with: y = 0.02 sin (125.7 - 502.7x) is that alright?
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    De Broglie wavelength calculations

    I had a go at 2 Q's and wanted to make sure I'm doing this right. so here's the first one, and maybe if i went wrong with it I was going to redo the 2nd Q on my own. \lambda = h/p = h/mv (\sqrt{1-((v^2)/(c^2))}) so, an Alpha Particle travelling @ 2x106m/s (mass = 6.645x10-27 kg)...
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    Another quick integration q

    the question is \int 2x sec^2 (x^2) dx do i sub u= sec (x^2) ? I so far have got to trying to sub u= sec(x^2) and getting du= 2 (sec x^2 tan x^2)... i have a strong feeling i fudged the "du" part. hmm.
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    Intergrating e

    intergrating "e" I'm doing some intergration q's and I'm stuck on one which involves e [x^2 e^(x^3) ]dx I know to integrate you "add one to the power and divide by the new power.. would that make the solution ((x^3)/3) ((e^(x^4))/(x^4)? hope that makes a bit of sense..
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    Consevation of energy in collisions

    I am going through some questions for resits in August, and I have no idea what this question is wanting me to explain : "Briefly discuss the circumstances under which (i) momentum, (ii) kinetic energy and (iii) total energy are conserved in collisions between two bodies. [3]" it's only a...