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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Vectors in Mechanics

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These notes are based on the requirements of the M5 A Level mathematics module.

Contents 1 Solution of simple vector differential equations 2 Work done by a constant force 3 Vector moment of a force 4 Resultant Force and Couples 5 Comments

Solution of simple vector differential equations

It’s the same as in previous modules (M3 and M4), where you had to solve scalar differential equations, but here you have vectors: all what you have to do is substitute

where u an w are scalars, so

, and

.

Now equate coefficients of i and j, solve a if it is a scalar equation, hence you can find u and w.

Work done by a constant force

All what you have to do is to find the scalar product of the Force vector and the Displacement vector. Of course to find the distance: position vector of final point - position vector of initial point.

Vector moment of a force

Where r is the position vector of any point on the line of action of F relative to the point where the moment is to be taken about.

Resultant Force and Couples

If a system of forces can be reduced to a resultant force, then G = 0

If a system of forces can be reduced into a couple of moment, then F_R = 0

A system s I equilibrium when both G and F_R are equal to zero.

It doesn’t matter about what point the resultant force is about. It’s the same about any point.

Comments

Originally written by yazan_l on TSR forums.