The Integrals of Mechanics |
Common terms and phrases
approximately base C₁ Calculus cardioid center of area center of mass coördinate planes cross section cycloid density varies diameter element of area ellipse equal equation Find the area Find the center Find the length find the moments Find the volume fixed plane formulæ given homogeneous right I₁ Illustrative example inertia with respect integration m₁ Ma² mass with respect mean density middle point moment of area moment of inertia momental ellipsoid moments of inertia moments of mass parabola y² paraboloid parallel parallelopiped plane area plane YZ polar coördinates products of inertia quadrant radii radius of inertia rectangular coördinates solid formed solid of revolution solid with respect square surface formed surface of revolution tangent theorem of Pappus thin plate triangle vertex volume and surface X-axis Y-axis πα
Popular passages
Page 47 - If a body is considered to be composed of a number of parts, its moment of inertia about an axis is equal to the sum of the moments of inertia of the...
Page 45 - The moment of inertia of an area with respect to any axis is equal to the moment of inertia with respect to a parallel axis through the...
Page 47 - I_ or: the polar moment of inertia is equal to the sum of the moments of inertia with respect to any two...
Page 43 - V is given either by the product of the charge and the potential difference or by one-half the product of the mass of the particle and the square of the final velocity. Solving (6-9) for the velocity, v = */-—— meters/sec (6-10) The energy acquired by an electron (e = 1.6 X 10"~l* coulomb) in "falling" through a potential difference of 1 volt is 1.6 X 10~
Page 47 - J of an area about a point is equal to the sum of the moments of inertia of the area about any two perpendicular axes in the area and passing through the same point.
Page 41 - The arc of the cycloid x = a (6 — sin 0), y = a (1 — cos 6) from 9 = 00 to 8 — 9\ ; (6) a complete arch of this cycloid.
Page 15 - ... difformity is of the first species," ie, the density varies as the distance from one edge. He shows that, if the difformity is of the Hth species, ie, if the density varies as the nth power of the distance from the...
Page 41 - — ; ie one half of the volume of the circumscribing cylinder. 6. Show that the volumes generated by revolving y = e1 about OJT and 01