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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. • Newton’s three laws of motion.

    2. • Forces as interactions between bodies.

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

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

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

    6. • Normal force FN acts perpendicular to the contact surface.

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

    8. • Tension.

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

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

    11. • Buoyancy from displaced fluid: Fb = ρVg.

    12. • Know field forces: gravitational, electric and magnetic.

    13. • Weight is gravitational force: Fg = mg.

    14. • Electric force Fe.

    15. • Magnetic force Fm.

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

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

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

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

    20. • Elastic and inelastic collisions of two bodies.

    21. • Explosions.

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

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

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

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

    26. • 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. A.3.1—Conservation of energy

      • Principle of the conservation of energy.

    2. A.3.2—Work as energy transfer

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

    3. A.3.3—Sankey diagrams

      • Energy transfers can be represented on a Sankey diagram.

    4. A.3.4—Work by constant force

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

    5. A.3.5—Work-energy change

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

    6. A.3.6—Mechanical energy

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

    7. A.3.7—Mechanical energy conservation

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

    8. A.3.8—Mechanical energy transformations

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

    9. A.3.9—Kinetic energy

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

    10. A.3.10—Gravitational potential energy

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

    11. A.3.11—Elastic potential energy

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

    12. A.3.12—Power

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

    13. A.3.13—Efficiency

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

    14. A.3.14—Fuel energy density

      • Energy density of the fuel sources.

  4. A.4 Rigid body mechanics

    1. • Torque about an axis: τ = Fr sin θ.

    2. • Bodies in rotational equilibrium have a resultant torque of zero.

    3. • An unbalanced torque applied to an extended, rigid body will cause angular acceleration.

    4. • The rotation of a body can be described: angular displacement, angular velocity and angular acceleration.

    5. • Use rotational SUVAT equations under uniform angular acceleration. • Variables include θ/Δθ, angular speed ω and angular acceleration α.

    6. • Moment of inertia depends on mass distribution about the rotation axis.

    7. • Point-mass moment of inertia: I = Σmr^2.

    8. • Rotational Newton’s second law: τ = Iα.

    9. • Angular momentum of a rotating body: L = Iω.

    10. • Angular momentum remains constant unless the body is acted upon by a resultant torque.

    11. • Angular impulse changes angular momentum: ΔL = τΔt = Δ(Iω).

    12. • Rotational kinetic energy: Ek = 1/2Iω^2 = L^2/2I.

  5. A.5 Galilean and special relativity

    1. • Reference frames.

    2. • Galilean relativity: Newton’s laws are identical in all inertial frames.

    3. • Galilean transformations: x′=x-vt and t′=t.

    4. • Galilean velocity addition: u′=u-v.

    5. • Two postulates of special relativity.

    6. • Lorentz transformations relate event coordinates between inertial frames. • Use γ and the two inertial-frame coordinates x, t and x′, t′.

    7. • Relativistic velocity addition: u′=(u-v)/(1-uv/c^2).

    8. • Space-time interval is invariant: (Δs)^2=(cΔt)^2-(Δx)^2.

    9. • Proper time interval and proper length.

    10. • Time dilation: Δt = γΔt0.

    11. • Length contraction: L = L0/γ.

    12. • Relativity of simultaneity.

    13. • Space-time diagrams.

    14. • On space-time diagrams, world-line angle relates to speed: tan θ = v/c.

    15. • Muon decay is experimental evidence for time dilation and length contraction.