← Mathematics of Mechanics syllabus

ScotlandMathematics of Mechanics

Force, Energy and Periodic Motion

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

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.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on circular motion, covering angular velocity, centripetal acceleration and force, the conical pendulum, banked tracks, motion in a vertical circle, and Newton's inverse-square law of gravitation with orbital motion.
14 min answer →

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.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on momentum and impulse, covering linear momentum, the impulse-momentum principle, the impulse of a variable force as an integral, conservation of momentum in direct collisions, and impulsive tensions in connected particles.
12 min answer →

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.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on rectilinear motion governed by differential equations, covering the three forms of acceleration, setting up the equation of motion for a variable force, solving by separation, motion against resistance, and finding the terminal velocity.
14 min answer →

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.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on simple harmonic motion, covering the defining equation, the displacement and velocity solutions, the period and amplitude, Hooke's law for springs and elastic strings, and the interchange of kinetic and potential energy in an oscillation.
14 min answer →

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.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on work, energy and power, covering the work done by a constant or variable force, kinetic and gravitational potential energy, the work-energy principle, conservation of mechanical energy, and the calculation of power.
13 min answer →