# Momental sentence example

momental

- Since they are essentially positive the quadric is an ellipsoid; it is called the momental ellipsoid at 0.
- A limitation is thus imposed on the possible forms of the momental ellipsoid; e.g.
- If all the masses lie in a plane (1=0) we have, in the notation of (25), c2 = o, and therefore A = Mb, B = Ma, C = M (a +b), so that the equation of the momental ellipsoid takes the form b2x2+a y2+(a2+b2) z1=s4.
- It possesses thi property that the radius of gyration about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points.
- The relation between these axes may be expressed by means of the momental ellipsoid at 0.Advertisement
- If p be the radius-vector 0J of the momental ellipsoid Ax+By+Czf=Me4 (I)
- The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.
- If A = B = C, the momental ellipsoid becomes a sphere; all axes through 0 are then principal axes, and the moment of inertia is the same for each.
- This shows that the C.P. is the antipole of the line of intersection of its plane with the free surface with respect to the momental ellipse at the C.G.