/sci/ - Science & Math

>>11614476
/mass/ moment of inertia AKA moment of inertia is [math] \int r^2\text{ d}m [/math]. it measures how hard it is change angular momentum of an object. analogous to mass. units of slug-inches-squared. there's a scalar MoI associated with each axis of a reference coordinate system affixed the object you care about, you can write it as a tensor
/area/ moment of inertia AKA second moment of area is [math] \int r^2\text{ d}A [/math]. it measures out rigid a shape in the plane. this is a strictly geometric thing. units of inches-to-the-fourth. see parallel and perpendicular axis thms.
>>11614123
The very first term in the original sum should make you worried, because you should know off the top of your head that the harmonic series diverges; this is just a multiple of the harmonic series. so with that hint, maybe look at some multiple of the harmonic series to compare the whole sum to. every term in S is greater than the associated term in 1/2n
>>11614476
>>11614540
SA of a body of rotation is circumference times length, right? or the [math] 2\pi f(x)\Delta\ell [/math]. dL is not a change in x; it is small length of the arc. Realize [math] d\ell=\sqrt{dx^2+dy^2}=\sqrt{1+[f'(x)]^2}dx [/math] and take the integral in your posts to be the sum under the proper limit
>>11614905
>supposing x^2-D has a root, then D is positive and also p(x) has two roots as given by quadratic formula
>supposing p(x) has two roots you can isolate D from quadratic formula and realize the square of any number is positive
>>11615188
why are you shoving foil into your bong what in the fuck
>>11615298
sadiku
>>11613998
>>11615178
>>11615229
>a
given: L=1.5 meters
>b
90 cm is 9/15 wavelengths so T=0.60*15/9=1 second
>c
T
>d
f==1/T
>e
v==L/T=Lf; 1.5 m/s = (1.5 m)(1 s)^-1
>>11615158
>Morris Kline has seems highly recommended and it's pretty cheap
its probably fine