Mechanics – Teacher Mathematics

Prerequisite Knowledge & Key Points

Solve Quadratic Equations by Factorization or Formula

Linear Simultaneous Equation

Equations of Constant Acceleration (5 SUVAT)

Distance - time Graph (Gradient)

Velocity - time Graph (Gradient, Area)

Pythagoras' Theorem

Trigonometry of Right-angled triangles

Sine Rule and Cosine Rule

Given one Trig Ratio, finding others

sine^2 x + con^2 x (trig identity)

tan x = sine x / cos x

Definition of Force, F=ma

Weight, w = mg

Reaction of Force or Normal

Resolution of Forces (Triangle Law of Vectors Addition)

Direction choices are usually Horizontally and Vertically, Parallel and Perpendicular to slope, or Parallel and Perpendicular to direction of motion

Resolving perpendicular to an unknown force means the unknown will not appear in the equation.

When direction of acceleration is unknown, it is normally best to find components of a resultant force and use them to find direction of magnitude of resultant.

Force resolution and Newton Second Law

Limiting Friction and R, mu

Total contact force is the combination of normal contact force and friction

If situation becomes different because a force a force changes or direction of motion switches, the normal contact force may be affected, so the friction may change. It is best to draw a new diagram every time a different situation arises.

Resolve forces in equilibrium and deal with non-equilibrium problems.

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Velocity is not the only measure of the MOTION OF AN OBJECT. We use acceleration to measure how quickly velocity is changing.

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Mid-Point and Length (Distance Formula) of Line Segment

Gradient of Parallel and Perpendicular Lines

Interpret y-y1=m(x-x1) and y = mx + c (gradient, y & x - intercept)

Completing the Square and solve

Surds

Equations of Circle in Standard and General Form

Angle Properties of Circle

Discriminant

Simultaneous Equations (2 & 3)

Solution of Simultaneous Equations and Points of Intersection on Graph

Points that lie on graph can be put (Satisfy or Balance) into its equation

Forces and Equilibrium

Kinematics

Rectilinear Motion - Motion on only one co-ordinate axis along with time

Kinematics deals with equation that describe the motion of objects without reference to forces.

Dynamics is the study of effect that forces and their influence on motion of objects.

Motion equation can be used both in space and on the Earth. On earth, we make approximation since there are greater number of variables like friction and atmosphere that effect motion in various ways.

Acceleration always have constant value, positive, negative or zero, since we won't look forces that could cause acceleration to change over time.

At Rest and at maximum and constant speed, acceleration is zero.

In convention, Right and Upward is take positive directions.

In straight line motion, we ignore direction. So we use speed, distance instead of velocity and displacement.

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