| George Atwood - Physics - 1784 - 284 pages
...• the diftance A-fB + C ^.xA+B+C of the centre of ofcillation from the axis of motion. The diftance of the centre of gyration from the axis of motion is a mean proportional between the diftances of the centres of ofcillation and gravity from the fame axis. The centre of percuffion is... | |
| Agriculture - 1810 - 606 pages
...g the distance between the centre •of gyration and the axis of motion. Now it is well known that the distance of the centre of gyration from the axis of motion is equal to the square root of the quotient, obtained by multiplying each particle in the balance by the... | |
| William Marrat - Mechanics - 1810 - 512 pages
...from the. axis of motion, be divided by the body or mass ; the square root of the quotient toil! be the distance of the centre of gyration from the axis of motion. Conceive the body to be made up of any number of particles A, B, D, Arc. and let the distances of these... | |
| Charles Hutton - Mathematics - 1811 - 404 pages
...PROPOSITION v. Given the radius R of a wheel, and the radius r, of its axle, the •weight of both, w, and the distance of the centre of gyration from the axis of motion, g ; also a givtn power p acting at the circumference of the wheel; to find the weight w raised by a... | |
| Charles Hutton - Mathematics - 1812 - 624 pages
...PROPOSITIOK v. Given the radius R of a wheel, and the radius r, of its axie, the weight of both, <w, and the distance of the centre of gyration from the axis of motion, j ; also a given fioner p acting at the circumference of the •wheel ; to find the weight w raised... | |
| Peter Barlow - Mathematics - 1814 - 426 pages
...semi-sphere or semi-spheroid со = Jo. 6. Paraboloid = Ja. LXXXVII. Of the Centre of Gyration. Let 8R denote the distance of the centre of gyration from the axis of motion; then ./ ~ - — ; where s denotes the body, and s its fluxion, at the distance x from the axis. Hence... | |
| Olinthus Gregory - Mechanical engineering - 1815 - 604 pages
...2-) w''l ke transformed to and these by the.def. must be equal. Consequently, B-CRI= and CR = COR. 1. The distance of the centre of gyration from the axis...proportional between the distances of the centres of oscillation and gravity, from the same axis. ForcR*=— — , while co=-^-; therefore co-ccn *£B '... | |
| James Mitchell - Mathematics - 1823 - 666 pages
...radius X \/§. A globe, abuul the diameter. = radius X v'g. In a cone, about the axis = radius XV$The distance of the centre of gyration from the axis of motion, is a mean proportional between the distance of the centre of gravity and centre of oscillation from the same axis. Hence, when any two... | |
| Dionysius Lardner - Geometry, Algebraic - 1823 - 658 pages
...of its definition, we find where м expresses the mass of the body. Hence, that is, " the square of the distance of the centre of gyration from the axis of motion is found by dividing the moment of inertia by the mass of the body." It appears, therefore, that the same... | |
| William Emerson - Mechanical engineering - 1825 - 506 pages
...same. For (by Cor. 6. Prop. XLIV.) the quantity A x SA2 + B x SB5 + CX SC2 will be given. Cor. 4. Tlie distance of the centre of gyration from the axis of...centres of gravity and percussion from that axis. It follows from this and the last Prop. Cor. 5. The momentum or quantity of motion of the whole system,... | |
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