Search results
Results From The WOW.Com Content Network
The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force is perpendicular to the displacement vector r, the moment arm will be equal to the distance to the centre, and torque will be a maximum for the given force. The ...
A continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Classical Momentum is a vector quantity : it has both magnitude and direction.
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs.
Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [ 9 ] : 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions.
The equation for universal gravitation thus takes the form: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses , and G is the gravitational constant .
The inverse cube nature of this equation is more readily seen by expressing the location vector as the product of its magnitude times the unit vector in its direction (= | | ^) so that: = ^ (^) | |. The equivalent equations for the magnetic B {\displaystyle \mathbf {B} } -field are the same except for a multiplicative factor of μ 0 = 4 π × ...
Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N) , and force is often represented by the symbol F . Force plays an important role in classical mechanics.
This matrix equation relates the scalar components of a in the n basis (u,v, and w) with those in the e basis (p, q, and r). Each matrix element c jk is the direction cosine relating n j to e k. [19] The term direction cosine refers to the cosine of the angle between two unit vectors, which is also equal to their dot product. [19] Therefore,