Maths YMA01 — specification explorer

1. Mathematical models in mechanics

• 1.1The basic ideas of mathematical modelling as applied in Mechanics. Students should be familiar with the terms: particle, lamina, rigid body, rod (light, uniform, non-uniform), inextensible string, smooth and rough surface, light smooth pulley, bead, wire, peg. Students should be familiar with the assumptions made in using these models.M1

1. Vectors in mechanics

• 2.1

  Magnitude and direction of a vector. Resultant of vectors may also be required.:

  • Students may be required to resolve a vector into two components or use a vector diagram. Questions may be set involving the unit vectors i and j.
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• 2.2

  Application of vectors to displacements, velocities, accelerations and forces in a plane. ematics of a particle moving in a stra:

  • Use of velocity = change of displacement in the case of constant time velocity, and of acceleration = change of velocity in the time case of constant acceleration, will be required. ight line
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1. Kinematics of a particle moving in a straight line

• 3.1Motion in a straight line with constant acceleration. Graphical solutions may be required, including displacement-time, velocity-time, speed-time and acceleration-time graphs. Knowledge and use of formulae for constant acceleration will be required.M1

1. Dynamics of a particle moving in a straight line or plane

• 4.1

  The concept of a force. Newton’s laws of motion.:

  • Simple problems involving constant acceleration in scalar form or as a vector of the form ai + bj.
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• 4.2

  Simple applications including the motion of two connected particles.:

  • Problems may include (i) the motion of two connected particles moving in a straight line or under gravity when the forces on each particle are constant; problems involving smooth fixed pulleys and/or pegs may be set (ii) motion under a force which changes from one fixed value to another, e.g. a particle hitting the ground (iii) motion directly up or down a smooth or rough inclined plane.
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• 4.3Momentum and impulse. The impulse-momentum principle. The principle of conservation of momentum applied to two particles colliding directly. Knowledge of Newton’s law of restitution is not required. Problems will be confined to those of a one-dimensional nature.M1
• 4.4

  Coefficient of friction.:

  • An understanding of F = μR when a particle is moving.
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1. Statics of a particle

• 5.1Forces treated as vectors. Resolution of forces.M1
• 5.2Equilibrium of a particle under coplanar forces. Weight, normal reaction, tension and thrust, friction. Only simple cases of the application of the conditions for equilibrium to uncomplicated systems will be required.M1
• 5.3

  Coefficient of friction. ents:

  • An understanding of F µR in a situation of equilibrium.
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1. Moments

• 6.1Moment of a force. Simple problems involving coplanar parallel forces acting on a body and conditions for equilibrium in such situations.M1