Introduction to mechanics

Vector definition

A quantity that has both direction and magnitude

Scalar definition

A quantity that only has magnitude

Scalars

Speed, mass, time, energy, power

Vectors

Displacement, velocity, acceleration, force, weight

Resultant vector definition

The combined effect of all the vectors

Conditions for equilibrium of two or three coplanar forces acting on a point

Total resultant force = 0

Or

If the vector representing the forced are added together they will form a closed triangle

Conditions for body to remain in equilibrium

• Resultant forcing acting on body is 0

• Resultant moment about any point is 0

(Object could be stationary or travelling at a constant velocity)

Moment definition

The turning effect of a force

Moment calculation

Force X perpendicular distance from the point to the line of action of the force. Moment = Fd

Units of moment

Nm

Principle of moments

In equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments

Couple definition

A pair of equal and opposite coplanar forces

Features of a couple

• Equal magnitude, act parallel to each other, but in opposite directions

• Don't cause any resultant linear force but does produce a turning effect

• Moment of a couple = force X perpendicular distance between the line of action and the forces

Centre of mass definition

Point in a body through which weight appears to act

Or

Point in a body where the resultant moment is zero

When will an object topple

If a vertical line drawn downwards from it's centre of mass falls outside it's base area

Why do objects topple

• A resultant moment occurs which provides a turning force

• An object is more stable with a low centre of mass and a wide base area

Stable equilibrium definition

When a body is displaced then released, it will return to it's equilibrium position

Unstable equilibrium definition

When a body is displaced then released, it will not return to it's equilibrium position

Displacement definition

Distance in a given direction

Velocity definition, units and formula

Rate of change of displacement, ms^-1

V = ∆s / ∆t

Acceleration definition, units and formula

Rate of change of velocity, ms^-2

a = ∆v / ∆t

Deceleration

When acceleration is in the opposite direction to the velocity, reducing the magnitude of the velocity. Velocity decreases with time

Average velocity formula

Total displacement (m) / total time (s)

define the moment of a force about a point

force multiplied by perpendicular distance between the line of action of the force and the point