β Scotland Mathematics of Mechanics
Scotland Β· SQASyllabus
Mathematics of Mechanics syllabus, dot point by dot point
Every dot point in the Scotland Mathematics of Mechanicssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Force, Energy and Periodic Motion
Module overview β- How do you analyse motion in a circle, and how do circular-motion ideas explain the conical pendulum, banked tracks, vertical circles and orbits under gravity?Analyse circular motion using angular velocity and centripetal acceleration; apply Newton's second law radially to the conical pendulum, banked tracks and motion in a vertical circle; and model gravitation with the inverse-square law.14 min answer β
- What are momentum and impulse, and how do you use conservation of momentum to analyse collisions and impulsive forces?Define linear momentum and impulse; relate impulse to change of momentum; apply conservation of linear momentum to direct collisions; and handle impulsive tensions in connected bodies.12 min answer β
- How do you analyse straight-line motion when the force varies with time, velocity or position, and how do differential equations give the motion and the terminal velocity?Set up and solve differential equations for rectilinear motion under a variable force; use the forms of acceleration as a function of t, v or x; and find terminal velocity for motion against resistance.14 min answer β
- What is simple harmonic motion, and how do you find the period, speed and displacement of an oscillating body, including a mass on a spring obeying Hooke's law?Define simple harmonic motion by the equation a equals minus omega squared x; derive and use the displacement, velocity and period results; apply Hooke's law to springs and strings; and analyse the energy of an oscillation.14 min answer β
- How do you calculate work, kinetic and potential energy and power, and how does the work-energy principle let you solve motion problems without finding the acceleration?Calculate the work done by a force, kinetic energy and gravitational potential energy; apply the work-energy principle and conservation of mechanical energy; and calculate power.13 min answer β
Linear and Parabolic Motion
Module overview β- How do Newton's laws relate force and motion, and how do you analyse equilibrium, friction, inclined planes and connected particles?Apply Newton's three laws of motion; draw free-body diagrams; resolve forces; analyse equilibrium, friction, motion on inclined planes, and systems of connected particles.14 min answer β
- How do you describe straight-line motion, and how do calculus and the constant-acceleration equations connect displacement, velocity and acceleration?Work with rectilinear motion: relate displacement, velocity and acceleration by differentiation and integration, use the equations of motion for constant acceleration, and interpret motion-time graphs.12 min answer β
- How do you describe motion in two or three dimensions using vector functions, and how do you find relative velocity, closest approach and whether two bodies collide?Use position, velocity and acceleration vectors as functions of time; calculate relative velocity; and find the closest approach of two moving bodies and the condition for collision.13 min answer β
- How do you model a projectile moving under gravity, and how do you find its range, maximum height, time of flight and path?Model projectile motion under gravity by treating horizontal and vertical motion independently; find time of flight, range, maximum height, velocity at any time, and the equation of the parabolic path.13 min answer β