Unit M3: Mechanics 3

Kinematics of a particle moving in The setting up and solution of equations where a straight line when the acceleration dv dv dx dx is a function of the displacement = f(t), v = f(x), = f(x) or = f(t) dt dx dt dt (x), or time (t). will be consistent with the level of calculus required in units P1, P2, P3 and P4.

Use kinematics of a particle moving to connect the rule to the data and decision in the question.

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

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

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

Elastic strings and springs.; Hooke’s law.

Use elastic strings and springs to connect the rule to the data and decision in the question.

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

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

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

Energy stored in an elastic string or Simple problems using the work-energy principle involving spring. kinetic energy, potential energy and elastic energy.

Use energy stored in elastic strings and springs to connect the rule to the data and decision in the question.

This matters because energy stored in elastic strings and springs determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply energy stored in elastic strings and springs to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Energy stored in elastic strings and springs is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Newton’s laws of motion, for a The solution of the resulting equations will be consistent particle moving in one dimension, with the level of calculus in units P1, P2, P3 and P4. when the applied force is variable.; Problems may involve the law of gravitation, i.e. the inverse square law.

Use variable-force motion in one dimension to connect the rule to the data and decision in the question.

This matters because variable-force motion in one dimension determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply variable-force motion in one dimension to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Variable-force motion in one dimension is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Prove that motion is simple harmonic by showing acceleration has the form x¨ = −ω²x, and solve SHM problems using geometric or calculus methods and standard formulae.

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

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

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

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

Oscillations of a particle attached to Oscillations will be in the direction of the string or spring the end of an elastic string or only. spring.

Use oscillations attached to elastic strings or springs to connect the rule to the data and decision in the question.

This matters because oscillations attached to elastic strings or springs determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply oscillations attached to elastic strings or springs to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Oscillations attached to elastic strings or springs is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Angular speed.; Radial acceleration in circular v2.

Use angular speed to connect the rule to the data and decision in the question.

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

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

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

motion.; The forms rω 2 and are r required.

Use motion to connect the rule to the data and decision in the question.

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

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

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

Uniform motion of a particle Problems involving the ‘conical pendulum’, an elastic moving in a horizontal circle. string, motion on a banked surface, as well as other contexts, may be set.

Use uniform motion of a particle to connect the rule to the data and decision in the question.

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

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

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

Motion of a particle in a vertical circle.

Use motion of a particle in a vertical circle to connect the rule to the data and decision in the question.

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

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

Boundary: Motion of a particle in a vertical circle is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Centre of mass of uniform rigid The use of integration and /or symmetry to determine the bodies and simple composite centre of mass of a uniform body will be required. bodies.

Use centre of mass of uniform rigid to connect the rule to the data and decision in the question.

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

Example: apply centre of mass of uniform rigid to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Centre of mass of uniform rigid is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Simple cases of equilibrium of rigid To include bodies. (i) suspension of a body from a fixed point, (ii) a rigid body placed on a horizontal or inclined plane.

Use simple cases of equilibrium of rigid to connect the rule to the data and decision in the question.

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

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

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