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A. Space, time and motion

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  1. A.1 Kinematics

    1. • Describe motion using position, velocity and acceleration.

    2. • Velocity is the rate of change of position, and acceleration is the rate of change of velocity.

    3. • Change in position is the displacement.

    4. • Distinguish distance and displacement.

    5. • Distinguish instantaneous vs average speed, velocity and acceleration.

    6. • Use SUVAT equations for uniform acceleration: s=(u+v)t/2; v=u+at; s=ut+1/2at^2; v^2=u^2+2as. • Apply only to uniformly accelerated motion.

    7. • Motion with uniform and non-uniform acceleration.

    8. • Resolve projectile motion into horizontal and vertical components when fluid resistance is absent.

    9. • Describe effects on trajectory, flight time, velocity, acceleration, range and terminal speed.

  2. A.2 Forces and momentum

    1. A.2.1—Newton’s three laws of motion

      • Newton’s three laws of motion.

    2. A.2.2—Forces as interactions between bodies

      • Forces as interactions between bodies.

    3. A.2.3—Free-body diagrams

      • Forces acting on a body can be represented in a free-body diagram.

    4. A.2.4—Resultant force from diagrams

      • Free-body diagrams can be analysed to find the resultant force on a system.

    5. A.2.5—Contact forces

      • Contact forces include normal, friction, tension, elastic restoring force, viscous drag and buoyancy.

    6. A.2.6—Normal force

      • Normal force FN acts perpendicular to the contact surface.

    7. A.2.7—Frictional force

      • Friction acts parallel to contact. • Static: Ff <= μsFN; dynamic: Ff = μdFN.

    8. A.2.8—Tension

      • Tension.

    9. A.2.9—Hooke’s law restoring force

      • Elastic restoring force follows Hooke’s law: FH = -kx.

    10. A.2.10—Viscous drag

      • Viscous drag on a small sphere: Fd = 6πηrv, opposite motion. • η is fluid viscosity, r sphere radius, v speed through fluid.

    11. A.2.11—Buoyancy

      • Buoyancy from displaced fluid: Fb = ρVg.

    12. A.2.12—Field forces

      • Know field forces: gravitational, electric and magnetic.

    13. A.2.13—Weight

      • Weight is gravitational force: Fg = mg.

    14. A.2.14—Electric force Fe

      • Electric force Fe.

    15. A.2.15—Magnetic force Fm

      • Magnetic force Fm.

    16. A.2.16—Linear momentum conservation

      • Linear momentum p=mv is conserved unless a resultant external force acts.

    17. A.2.17—Impulse

      • Impulse from resultant external force: J = FΔt = Δp.

    18. A.2.18—Impulse-momentum change

      • The applied external impulse equals the change in momentum of the system.

    19. A.2.19—Newton’s second law forms

      • Use F=ma for constant mass; use F=Δp/Δt when mass changes.

    20. A.2.20—Elastic and inelastic collisions

      • Elastic and inelastic collisions of two bodies.

    21. A.2.21—Explosions

      • Explosions.

    22. A.2.22—Collision energy

      • Compare energy in elastic collisions, inelastic collisions and explosions.

    23. A.2.23—Centripetal acceleration

      • Centripetal acceleration is radial: a=v^2/r=ω^2r=4π^2r/T^2. • Direction is radially toward the centre of the circle.

    24. A.2.24—Centripetal force

      • Circular motion is caused by a centripetal force acting perpendicular to the velocity.

    25. A.2.25—Direction change in circular motion

      • A centripetal force causes the body to change direction even if its magnitude of velocity may remain constant.

    26. A.2.26—Angular and linear speed

      • Circular motion relation: v=2πr/T=ωr. • Use angular velocity ω and period T to link angular and linear descriptions.

  3. A.3 Work, energy and power

    1. • Principle of the conservation of energy.

    2. • Work done by a force is equivalent to a transfer of energy.

    3. • Energy transfers can be represented on a Sankey diagram.

    4. • Work by constant force along displacement: W = Fs cos θ.

    5. • Work done by the resultant force on a system is equal to the change in the energy of the system.

    6. • Mechanical energy includes kinetic, gravitational potential and elastic potential energy.

    7. • Mechanical energy is conserved when friction/resistive forces are absent.

    8. • If mechanical energy is conserved, work transforms energy between mechanical forms. • Relevant forms: translational kinetic, near-Earth gravitational potential and elastic potential.

    9. • Translational kinetic energy: Ek = 1/2mv^2 = p^2/2m.

    10. • Near Earth, gravitational potential energy change: ΔEp = mgΔh.

    11. • Elastic potential energy: EH = 1/2k(Δx)^2.

    12. • Power is rate of work or energy transfer: P=ΔW/Δt=Fv.

    13. • Efficiency: η=Eoutput/Einput=Poutput/Pinput.

    14. • Energy density of the fuel sources.