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Advanced Higher Mechanics

Force, Energy, Motion, and Mathematical Techniques

Course Overview

This course is spread across three units:

Force, Energy and Periodic Motion (FEP)
Linear and Parabolic Motion (LPM)
Mathematical Techniques for Mechanics (MTM)

An external SQA exam is sat at the end of the course.

QS: Mechanics Scholar Advanced Higher Mechanics Past Papers

Higher Maths Advanced Higher Maths

Prerequisite Knowledge

You must have a good grasp of the following:

Linear & Parabolic Motion (LPM)

LPM 1.1: Motion in Straight Lines

Key subskills:
Working with time-dependent graphs.
Rates of change in one dimension.
Equations of motion under constant acceleration.

Reading graphs Areas of graphs Deriving Newton's equations Equations of motion

LPM 1.2: Vectors in Motion

Key subskills:
Displacement, velocity, acceleration vectors.
Resultant and relative velocity.
Relative motion.

Linear motion with bearings Vectors and bearings Relative motion Vectors and forces Law of Statics Single pulleys Pulleys

LPM 1.3: Projectiles

Key subskills:
Horizontal & vertical components.
Parabolic motion equations.

Projectile Motion Horizontal Range Parametric equations Uses of parametric equations

LPM 1.4: Forces & Equilibrium

Key subskills:
Newton’s laws.
Static/dynamic friction.
Equilibrium.

Newton's Laws Triangle of Forces Deriving Lami's Theorem Pulleys Single pulleys Inclined planes Coefficient of friction
Force, Energy & Periodic Motion (FEP)

FEP 1.1: Momentum, Impulse, Work & Energy

Key subskills:
Working with impulse and/or force as the rate of change of momentum.
Working with the concept of conservation of linear momentum.
Determining work done by a constant force in one or two dimensions, or a variable force during rectilinear motion.
Using the concepts of kinetic and/or potential energy

Linear Momentum Impulse Conservation of Momentum Hooke's Law Work Done Power Kinetic Energy Potential Energy

FEP 1.2: Horizontal Circular Motion

Key subskills:
Applying equations to motion in a horizontal circle with uniform angular velocity.
Using equations for horizontal circular motion alongside Newton's Inverse Square Law of Gravitation

Angular velocity derivation Angular velocity formulae Centripetal acceleration Uniform circular motion Conical Pendulums Banked Motion

FEP 1.3: Simple Harmonic Motion

Key subskills:
Working with the concept of Simple Harmonic Motion (SHM).
Applying Hooke's Law to problems involving Simple Harmonic Motion

Simple Harmonic Motion Hooke's Law & SHM

FEP 1.4: Centres of Mass

Key subskills:
Determining the turning effect of force.
Using moments to find the centre of mass of a body.

Turning moments Static rigid bodies Couples Centre of Mass
Mathematical Techniques for Mechanics (MTM)

MTM 1.1: Partial Fractions

Key subskills:
Expressing rational functions as a sum of partial fractions
(denominator of degree at most 3 and easily factorised)

Rational fractions Partial fractions Distinct linear factors Repeated linear factors Irreducible quadratic

MTM 1.2: Differentiation Techniques

Key subskills:
Differentiating exponential and logarithmic functions.
Differentiating functions using the chain rule
Differentiating functions given in the form of a product and/or in the form of a quotient.
Finding the derivative of functions defined implicitly.
Finding the derivatives of a function defined parametrically.

First principles xⁿ axⁿ Derivatives of sums Chain rule Product rule Quotient rule Trig functions Differentiation refresher Trig formulae refresher Higher derivatives Differentiation formulae Exponentials & logs Inverse functions Implicit & explicit Logarithmic functions Parametric equations Differentiating parametric Second derivative

MTM 1.3: Integration Techniques

Key subskills:
Integrating expressions using standard results.
ntegrating using a substitution when the substitution is given.
Integrating by parts.
Applying integration to a range of physical situations..

Integration refresher Areas under curves Area & x-axis Area & y-axis Standard integrals eˣ & 1/x Improper integrals sec²x Inverse trig integrals Rational functions Volumes of revolution Integration by substitution Integration by parts

MTM 1.4: Differential Equations

Key subskills:
Finding a general solution of a first order differential equation with variables separable.
Solving a simple first order linear differential equations using an integrating factor.
Solving second order homogeneous equations

Differential equations First-order DEs Second-order DEs. Applications
Useful Links
Maths.scot

Free Maths resources for Scottish Secondary students

Mrs Physics

Advanced Higher Physics

Free AdH Mechanics

national5maths.co.uk - Free AH Maths of Mechanics

Clelland Maths

An excellent app. National 5, Higher, Advanced Higher.

Books