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Topic 1: Motion and Relativity

10 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do Einstein's two postulates lead to the conclusion that time itself depends on relative motion?

State Einstein's postulates of special relativity and apply time dilation and length contraction to objects moving at relativistic speeds.

Einstein's two postulates of special relativity and how they lead to time dilation and length contraction, with the Lorentz factor and worked examples.

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Why does an object moving at constant speed in a circle still accelerate, and what force keeps it on the circular path?

Describe uniform circular motion using centripetal acceleration and force, relating them to speed, radius and period.

Why circular motion at constant speed is accelerated motion, how centripetal acceleration and force point toward the centre, and how to relate them to speed, radius and period.

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How does the impulse of a force change the momentum of an object?

Relate impulse to the change in momentum of an object using

\vec{J} = \vec{F}\Delta t = \Delta \vec{p}

, and interpret force-time graphs.

Defining momentum and impulse, the impulse-momentum theorem, reading impulse from a force-time graph, and how impulse explains safety features, with worked examples.

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Why is the total momentum of an isolated system the same before and after a collision, even when kinetic energy is lost?

Apply conservation of momentum to elastic and inelastic collisions in one dimension, and distinguish them using kinetic energy.

How conservation of momentum solves one-dimensional collisions, the difference between elastic and inelastic collisions, and why momentum is conserved while kinetic energy may not be.

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What does Einstein's equation $E = mc^2$ tell us about the relationship between mass and energy?

Apply mass-energy equivalence to rest energy and to the mass defect and energy release in nuclear processes.

How $E = mc^2$ expresses mass and energy as interchangeable, the meaning of rest energy, and how mass defect explains the energy released in nuclear reactions, with worked examples.

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How can the motion of a projectile be predicted by treating its horizontal and vertical motions independently?

Resolve projectile motion into independent horizontal (constant velocity) and vertical (constant acceleration) components to predict range, time of flight and maximum height.

How to model projectiles by separating horizontal constant-velocity motion from vertical constant-acceleration motion, with worked examples of range, time of flight and maximum height.

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How do work, kinetic energy and power describe the transfer and rate of transfer of energy in mechanical systems?

Calculate work done by a force, relate net work to change in kinetic energy via the work-energy theorem, and define power as the rate of doing work.

Defining mechanical work including the angle factor, the work-energy theorem linking net work to change in kinetic energy, and power as the rate of energy transfer, with worked examples.

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How does the gravitational attraction between two masses depend on their masses and separation?

Apply Newton's law of universal gravitation and the concept of gravitational field strength to interactions between masses.

Newton's inverse-square law of gravitation, how gravitational force depends on mass and separation, and the meaning of gravitational field strength, with worked examples.

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How do Newton's three laws relate the forces on an object to its motion?

Apply Newton's three laws of motion, drawing free-body diagrams and resolving forces to determine the acceleration of objects and the forces in interacting systems.

Newton's three laws of motion, free-body diagrams, resolving forces on inclines, connected systems, and using net force to find acceleration, with worked examples.

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What determines the speed and period of a satellite, and why does the same gravitational force produce a stable orbit?

Analyse the orbital motion of satellites by equating gravitational force to the centripetal force requirement, deriving orbital speed and period.

How gravity provides the centripetal force for a satellite, leading to expressions for orbital speed and period, Kepler's third law, and the idea of geostationary orbits.

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