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Mathematics of MechanicsQ&A by dot point

A short Q&A bank for every Scotland Mathematics of Mechanics syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.

Force, Energy and Periodic Motion

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.
2Q&A pairs
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.
2Q&A pairs
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.
3Q&A pairs
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.
2Q&A pairs
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.
3Q&A pairs

Linear and Parabolic Motion

Mathematical Techniques for Mechanics

Use the supporting mathematical toolkit for mechanics: vector algebra and the scalar product, differentiation and integration of the functions arising in motion, and the solution of the differential equations that model rectilinear motion.
2Q&A pairs