Advanced Higher Mechanics
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.
Prerequisite Knowledge
You must have a good grasp of the following :
- Differentiation.
- Integration.
- Manipulating Vectors.
- Algebraic manipulation.
LPM 1.1 : Applying skills to motion in a straight lines
Key subskills
Working with time-dependent graphs.
Working with rates of change with respect to time in one dimension.
Using equations of motion in one dimension under constant acceleration
LPM 1.2 : Applying skills to vectors associated with motion
Key subskills
Using vectors to define displacement, velocity and acceleration.
Finding resultant velocity, relative velocity or relative acceleration of one body with respect to another.
Applying understanding of relative motion.
LPM 1.3 :Applying skills to projectiles moving in a vertical plane.
Key subskills
Establishing the conditions of motion in horizontal and vertical directions involved in parabolic motion.
Using the equations of motion in parabolic flight.
LPM 1.4 :Applying skills to forces associated with dynamics and equilibrium.
Key subskills
Using Newton’s first and third laws of motion to understand equilibrium.
Understanding the concept of static friction, dynamic friction and limiting friction.
Using Newton’s second law of motion.
FEP 1.1 : Applying skills to principles of momentum, impulse, work, power and energy
Key subskills
Working with impulse as the change in momentum, 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 to applying the
work–energy principle.
Using the concepts of kinetic and/or potential energy within the concept
of conservation of energy
FEP 1.2 : Applying skills to motion in a horizontal circle with uniform angular velocity.
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.
FEP 1.3 :Applying skills to simple harmonic motion.
Key subskills
Working with the concept of Simple Harmonic Motion (SHM).
Applying Hooke's Law to problems involving Simple Harmonic Motion.
FEP 1.4 :Applying skills to centres of mass.
Key subskills
Determining the turning effect of force.
Using moments to find the centre of mass of a body.
MTM 1.1 : Applying algebraic skills to partial fractions.
Key subskills
Expressing rational functions as a sum of partial fractions
(denominator of degree at most 3 and easily factorised)
MTM 1.2 : Applying calculus skills through techniques of differentiation.
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
Differentiation Refresher
Rules
Parametric Differentiation
MTM 1.3 :Applying calculus skills through techniques of integration.
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.
MTM 1.4 :Applying calculus skills to solving 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
© Alexander Forrest