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In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. [1]: 39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. [1]: 45–46 [2]
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
There were significant reviews given near the time of original publication. G.J.Whitrow:. Although many books have been published in recent years in which vector and tensor methods are used for solving problems in geometry and mathematical physics, there has been a lack of first-class treatises which explain the methods in full detail and are nevertheless suitable for the undergraduate student.
A scalar is a quantity, whereas a vector is represented by quantity and direction. The results of these two different approaches are equivalent, but the analytical mechanics approach has many advantages for complex problems. Analytical mechanics takes advantage of a system's constraints to solve problems.
In vector format, the moment can be defined as the cross product between the radius vector, r ... Vector Mechanics for Engineers: Statics, 9th Ed. McGraw Hill.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body.
denotes the cross product, which produces a vector that is perpendicular both to r and to F following the right-hand rule, is the angle between the force vector and the lever arm vector. The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.
Momentum is a vector quantity, so impulse is also a vector quantity: ... Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, ...