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Unit M3: Mechanics 3

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  1. M3.1 - Further kinematics

    1. 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.

  2. M3.2 - Elastic strings and springs

    1. Elastic strings and springs.; Hooke’s law.

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

  3. M3.3 - Further dynamics

    1. M3.3.1Variable-force motion in one dimension

      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.

    2. M3.3.2Simple harmonic motion

      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.

    3. M3.3.3Oscillations attached to elastic strings or springs

      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.

  4. M3.4 - Motion in a circle

    1. Angular speed.; Radial acceleration in circular v2.

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

    3. 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.

    4. Motion of a particle in a vertical circle.

  5. M3.5 - Statics of rigid bodies

    1. 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.

    2. 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.