A. Space, time and motion

A.1.1—Position, velocity and acceleration

• Describe motion using position, velocity and acceleration.

A.1.2—Velocity and acceleration rates

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

A.1.3—Displacement

• Change in position is the displacement.

A.1.4—Distance and displacement

• Distinguish distance and displacement.

A.1.5—Instantaneous and average values

• Distinguish instantaneous vs average speed, velocity and acceleration.

A.1.6—Uniform acceleration equations

• 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.

A.1.7—Uniform vs non-uniform acceleration

• Motion with uniform and non-uniform acceleration.

A.1.8—Projectile components

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

A.1.9—Fluid resistance on projectiles

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

• Newton’s three laws of motion.

• Forces as interactions between bodies.

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

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

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

• Normal force FN acts perpendicular to the contact surface.

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

• Tension.

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

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

• Buoyancy from displaced fluid: Fb = ρVg.

• Know field forces: gravitational, electric and magnetic.

• Weight is gravitational force: Fg = mg.

• Electric force Fe.

• Magnetic force Fm.

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

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

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

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

• Elastic and inelastic collisions of two bodies.

• Explosions.

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

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

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

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

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

• Principle of the conservation of energy.

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

• Energy transfers can be represented on a Sankey diagram.

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

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

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

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

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

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

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

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

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

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

• Energy density of the fuel sources.

• Torque about an axis: τ = Fr sin θ.

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

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

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

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

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

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

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

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

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

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

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

• Reference frames.

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

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

• Galilean velocity addition: u′=u-v.

• Two postulates of special relativity.

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

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

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

• Proper time interval and proper length.

• Time dilation: Δt = γΔt0.

• Length contraction: L = L0/γ.

• Relativity of simultaneity.

• Space-time diagrams.

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

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