Unit M1: Mechanics 1

The basic ideas of mathematical Students should be familiar with the terms: particle, lamina, modelling as applied in Mechanics. 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.

Use basic ideas of mathematical to connect the rule to the data and decision in the question.

This matters because basic ideas of mathematical determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply basic ideas of mathematical to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Basic ideas of mathematical is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Magnitude and direction of a Students may be required to resolve a vector into two vector.; Resultant of vectors may components or use a vector diagram.; Questions may be set also be required. involving the unit vectors i and j.

Use magnitude and direction to connect the rule to the data and decision in the question.

This matters because magnitude and direction determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply magnitude and direction to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Magnitude and direction is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Application of vectors to Use of displacements, velocities, change of displacement accelerations and forces in a plane. velocity = in the case of constant time change of velocity velocity, and of acceleration = in the time case of constant acceleration, will be required.

Use application of vectors to connect the rule to the data and decision in the question.

This matters because application of vectors determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply application of vectors to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Application of vectors is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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

Use constant-acceleration motion in a straight line to connect the rule to the data and decision in the question.

This matters because constant-acceleration motion in a straight line determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply constant-acceleration motion in a straight line to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Constant-acceleration motion in a straight line is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The concept of a force.; Newton’s Simple problems involving constant acceleration in scalar laws of motion. form or as a vector of the form ai + bj.

Use concept of a force to connect the rule to the data and decision in the question.

This matters because concept of a force determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply concept of a force to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: concept of a force is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Simple applications including the Problems may include motion of two connected particles. (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.

Use simple applications to connect the rule to the data and decision in the question.

This matters because simple applications determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply simple applications to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Simple applications is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Momentum and impulse.; The Knowledge of Newton’s law of restitution is not required. impulse-momentum principle.; The Problems will be confined to those of a one-dimensional principle of conservation of nature. momentum applied to two particles colliding directly.

Use momentum and impulse to connect the rule to the data and decision in the question.

This matters because momentum and impulse determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply momentum and impulse to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Momentum and impulse is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Coefficient of friction.; An understanding of F = μR when a particle is moving.

Use coefficient of friction to connect the rule to the data and decision in the question.

This matters because coefficient of friction determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply coefficient of friction to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Coefficient of friction is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Forces treated as vectors.; Resolution of forces.

Use forces treated as vectors to connect the rule to the data and decision in the question.

This matters because forces treated as vectors determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply forces treated as vectors to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Forces treated as vectors is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Equilibrium of a particle under Only simple cases of the application of the conditions for coplanar forces.; Weight, normal equilibrium to uncomplicated systems will be required. reaction, tension and thrust, friction.

Use equilibrium of a particle under to connect the rule to the data and decision in the question.

This matters because equilibrium of a particle under determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply equilibrium of a particle under to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Equilibrium of a particle under is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use the coefficient of friction and the equilibrium condition F ≤ μR.

Use coefficient of friction to connect the rule to the data and decision in the question.

This matters because coefficient of friction determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply coefficient of friction to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Coefficient of friction is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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

Use moment of a force to connect the rule to the data and decision in the question.

This matters because moment of a force determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply moment of a force to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Moment of a force is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.