Theme A — Space, Time and Motion
Theme A — Space, Time and Motion — IB Physics HL Revision Notes & Topical Questions
5 min read 11 parts Lesson 1 of 63 Unit quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
Theme A — Space, Time and Motion — IB PHYSICS HL notes: Apply kinematics, drag, Newton's laws, circular motion, energy, rotational dynamics and special relativity to HL problems.Kinematics describes motion with displacement, velocity and acceleration, the suvat equations for unif…
- Laminar flow at low speed
- Turbulent flow at high speed or with blunt shapes
- For a sphere moving slowly in a viscous liquid Stokes' law Fd
- For a falling object Fnet
- Acceleration is proportional to resultant force and inversely proportional to mass
- Mass is the amount of matter (kg, scalar)
Part 1 of 9Kinematics and drag
1
Kinematics describes motion with displacement, velocity and acceleration, the suvat equations for uniform acceleration and projectile motion.
2
Drag
Drag the resistive force exerted by a fluid on a moving object.
- It depends on speed, cross-sectional area, shape, fluid properties and surface roughness.
- Denser or more viscous fluids give more drag; streamlined shapes reduce it.
3
Laminar flow at low speed
- Laminar flow at low speed drag is small and roughly proportional to speed.
4
Turbulent flow at high speed or with blunt shapes
- Turbulent flow at high speed or with blunt shapes a low-pressure wake forms and drag grows roughly as v2.
5
For a sphere moving slowly in a viscous liquid Stokes' law Fd
6πηrv applies.
6
For a falling object Fnet
For a falling object Fnet mg − Fdrag, so a = g − Fdrag/m, less than g.
- As speed rises drag grows until it balances weight, acceleration is zero and terminal speed is reached.
- A parachute increases area and reduces the terminal speed.
7
Drag reduces both horizontal and vertical speeds of a projectile.
Part 2 of 9Newton's second law and connected bodies
1
Acceleration is proportional to resultant force and inversely proportional to mass
- a = Fnet/m, along the resultant.
- Only the resultant matters — large balanced forces give zero acceleration.
2
Method for problems.
- Draw a free-body diagram.
- Find the resultant in the direction of motion.
- Divide by the mass of the whole system being accelerated.
3Mass is the amount of matter (kg, scalar)
- Mass is the amount of matter (kg, scalar) weight W = mg is a force (N, vector).
4In free fall mg
In free fall mg ma, so a = g for all masses.
5Connected masses m1 and m2
- Connected masses m1 and m2 the resultant external force is (m1 + m2)a, and tension comes from F = ma on one body.
6
On a slope the resultant is mg sin θ minus friction.
7In a lift accelerating upward T
In a lift accelerating upward T m(g + a), so passengers feel heavier.
8Experiment
- Experiment move masses between trolley and hanger to keep total mass constant.
- A graph of a against F is a straight line through the origin with gradient 1/m;
- compensate friction by tilting the runway.
Part 3 of 9Circular motion and momentum
1Angular velocity ω
2π/T = v/r.
2Centripetal acceleration a
Centripetal acceleration a v2/r = ω2r = 4π2r/T2, towards the centre.
3Centripetal force is the resultant of real forces
- Centripetal force is the resultant of real forces tension, friction, gravity or normal force.
- It does no work because it is perpendicular to the velocity.
4Momentum p
Momentum p mv is conserved in collisions and explosions when no external force acts.
- Impulse FΔt = Δp; F = Δp/Δt.What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
- In 2D each component is conserved separately.
Part 4 of 9Work, energy and power
Work, energy and power
Work W
Fs cos θ — the energy transferred by a force.
Energy cannot be created or destroyed, only transferred.
Net work done equals the change in kinetic energy.
Gravitational potential energy
- Gravitational potential energy stored by position in a gravitational field.
- It uses the field strength g (9.8 N kg-1 near Earth's surface) and a chosen zero level.
- Gravity is conservative because work depends only on end points.
- Pumped storage stores energy as GPE of water in an elevated reservoir.
Elastic potential energy EH
½k(Δx)2, the area under the force–extension graph.
Power P
ΔW/Δt = Fv; efficiency = useful output / total input.
Mechanical energy Ek + Ep + EH is conserved when no resistive forces act.
Part 5 of 9Rotational dynamics
1Torque τ
Fr sin θ — a couple has zero resultant force but a net torque.
2Body in equilibrium
- Body in equilibrium net torque is zero about every point, so any pivot may be chosen.
- Choose a point through which unknown forces act so they drop out.
- For a hinged beam, choosing the hinge removes the unknown hinge force.
3τ
Iα — moment of inertia I = Σmr2, in kg m2.
4Angular momentum L
Iω (kg m2 s-1); for a point mass L = mvr; for circular motion L = mr2ω.
- Conserved when no net torque actsIiωi = Ifωf.
5Angular impulse τΔt
ΔL — the area under a torque–time graph.
6Rotational kinetic energy ½Iω2
- Rotational kinetic energy ½Iω2 a rolling solid cylinder has total kinetic energy ¾mv2.
Part 6 of 9Galilean relativity and reference frames
1
A closed cabin gives no mechanical experiment that can tell rest from constant velocity (Galileo).
2Principle of relativity
- Principle of relativity the laws of mechanics have the same form in all inertial frames, so there is no absolute rest.
3Galilean transformations: x'
Galilean transformations: x' x − vt, t' = t, u' = u − v.
4
Valid for v much less than c.
Part 7 of 9Special relativity
| Feature | Galilean | Special relativity |
|---|---|---|
| Time | Absolute | Depends on observer |
| Velocity addition | u' = u − v | u' = (u − v)/(1 − uv/c2) |
| Speed of light | Depends on observer | Same for all inertial observers |
| Valid when | v much less than c | All speeds |
1Postulates
- Postulates laws of physics are the same in all inertial frames, and the speed of light is the same for all.
2Lorentz factor γ
1/√(1 − v2/c2).
- Time dilation Δt = γΔt0; length contraction L = L0/γ.
3Lorentz transformation Δt'
γ(Δt − vΔx/c2).
- If events are simultaneous in S, Δt' = −γvΔx/c2.
4Space-time interval (Δs)2
(cΔt)2 − (Δx)2 is invariant.
- Time-like or space-like separation matters for causality.
Part 8 of 9Answering relativity questions
Describe an observer in each frame and state that light travels at c in both.
Say how moving receivers meet the light at different times.
Use the phrase "in the frame of..." for each measurement.
Identify the proper time (events at the same place) and the proper length (object at rest).
Space-time diagrams
- Space-time diagrams world lines are steeper than the light line of gradient 1.
Part 9 of 9More from the specification
More from the specification
Inertial frames of reference
- An inertial reference frame is one in which Newton's first law holds true, moving at constant velocity with zero linear acceleration.
Relative velocity in one dimension
- The velocity of an object A relative to observer B is given by vector subtraction: vAB = vA - vB, depending on the chosen reference frame.
Galilean relativity principles
- The fundamental laws of Newtonian mechanics take the exact same mathematical form in all inertial reference frames.
Muon decay time dilation
- Muon decay time dilation high-speed atmospheric muons survive to Earth surface because relativistic speed dilates their lifetime in the ground frame.
Inertial frames of reference
- Inertial frames of reference observers moving at constant velocity measure physical laws identically without detecting fictitious inertial forces.
Spacetime interval preservation
- Spacetime interval preservation invariant spacetime intervals ensure all inertial observers calculate identical physical intervals despite relative motion.
Stationary
- Not moving.
Distance
- Total length of path travelled, a scalar.
Reference frame
- Coordinate system used by an observer.
Key terms
| Term | Meaning |
|---|---|
| Terminal speed | Constant speed reached when drag equals weight. |
| Centripetal acceleration | Acceleration towards the centre of a circle, v2/r. |
| Angular momentum | L = Iω, rotational analogue of linear momentum. |
| Moment of inertia | Resistance to angular acceleration. |
| Inertial frame | Frame of reference with no acceleration. |
| Lorentz factor | γ = 1/√(1 − v2/c2. |
| Conservative force | Force for which work depends only on the end points. |
Avoid these mistakes
1
Assuming the normal force always equals mg, or treating it as the third-law partner of weight.
2
Believing tension changes as a string passes over a smooth pulley, or that a surface can pull an object.
3
Calling centripetal force a separate force rather than the resultant of real forces.
4
Forgetting to divide by the mass of the whole system when using F = ma on connected bodies.
5
Using Galilean velocity addition at speeds close to c.
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Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).