Physics - Motion and Relativity - Fundamentals

32 concise fundamentals covering projectiles, momentum, circular motion, gravity and relativity.

Vectors | How are scalars and vectors different?

A scalar has size only, such as mass or speed. A vector also has direction, such as displacement, velocity or force.

Motion | How do distance, displacement, speed and velocity differ?

Distance is total path length; displacement is change in position. Speed is distance per second; velocity is displacement per second, including direction.

Motion | What does acceleration mean?

The rate of change of velocity: a = Δv/Δt. A change in speed, direction or both is acceleration. Its unit is m/s².

Motion | What do motion-graph gradients and areas tell you?

Displacement-time gradient gives velocity. Velocity-time gradient gives acceleration; signed area gives displacement. Acceleration-time signed area gives change in velocity.

Projectiles | Why can horizontal and vertical motion be treated separately?

They are perpendicular components of the same motion. Without air resistance, horizontal acceleration is zero and vertical acceleration is g downwards. Both components share the same time.

Projectiles | How do you split a launch velocity into components?

For angle θ above the horizontal: uₓ = u cosθ and uᵧ = u sinθ. Recombine using v = √(vₓ² + vᵧ²), then use the signs to choose the correct direction.

Projectiles | When can you use the constant-acceleration equations?

When acceleration is constant: v = u + at; s = ut + ½at²; v² = u² + 2as. Use each direction separately and keep one sign convention.

Projectiles | What happens at the highest point?

Vertical velocity is zero for an upward-launched projectile. Horizontal velocity remains unchanged without drag. Acceleration is still g downwards, not zero.

Projectiles | What sets range and flight time?

Range = horizontal velocity × flight time. Vertical motion sets the time. At equal launch/landing heights and no drag, 45° gives maximum range; complementary angles give equal ranges at the same speed.

Drag | What affects air resistance?

Drag opposes motion through the air. It generally increases with speed, cross-sectional area and air density; shape also matters. It reduces a projectile's range and maximum height.

Drag | What is terminal velocity?

A steady falling velocity reached when upward drag balances weight. Net force and acceleration are zero, although the object is still moving.

Forces | What do Newton's three laws say?

1: Zero net force means constant velocity. 2: Net force F = ma. 3: Interacting objects exert equal and opposite forces on each other; the pair acts on different objects.

Momentum | What are momentum and impulse?

Momentum p = mv is a vector. Impulse is change in momentum: Δp = FavgΔt. For the same momentum change, a longer stopping time gives a smaller average force.

Momentum | When is momentum conserved?

When the system has no net external impulse. Total vector momentum before equals total vector momentum after. Apply this separately in each direction.

Momentum | How do elastic and inelastic collisions differ?

Both conserve total momentum in an isolated system. Elastic collisions also conserve total kinetic energy. Inelastic collisions convert some kinetic energy into other forms; sticking together is perfectly inelastic.

Momentum | Why can a rocket accelerate in empty space?

It ejects gas backwards. The gas gains backward momentum, so the rocket gains forward momentum. It does not need air to push against.

Momentum | Why does reflection push a solar sail more than absorption?

Reflection reverses the photon's momentum component perpendicular to the sail. This gives a larger momentum change than stopping that component by absorption, so the sail receives a larger impulse.

Circular motion | Why is constant-speed circular motion accelerating?

Velocity keeps changing direction. The acceleration points towards the centre: a = v²/r. Velocity points along the tangent.

Circular motion | What is centripetal force?

The inward net force needed for circular motion: Fnet = mv²/r. It is supplied by actual forces such as tension, friction or gravity; it is not an extra force to add.

Circular motion | How are speed, period and frequency connected?

Period T is time for one revolution; frequency f is revolutions per second. v = 2πr/T and f = 1/T.

Circular motion | Why are corners banked?

The normal force tilts inwards. Its horizontal component helps supply the centripetal force, reducing reliance on friction. Its vertical component helps balance weight.

Gravity | What do gravitational force and field strength mean?

F = GMm/r² is the attraction between masses. g = F/m = GM/r² is force per kilogram, in N/kg, and equals free-fall acceleration. r is measured from the centre of a spherical body.

Gravity | How does distance affect gravity?

Gravity follows an inverse-square law. Doubling centre-to-centre distance makes the force one quarter as large. The two objects still exert equal and opposite forces.

Orbits | Why does a satellite stay in orbit?

Gravity continuously curves its path towards the central body while it moves sideways. It is in free fall. For a circular orbit, gravity supplies mv²/r.

Orbits | What determines circular orbital speed and period?

v = √(GM/r) and T = 2πr/v. They depend on orbital radius and central mass, not satellite mass. A higher circular orbit has lower speed and a longer period; r = planet radius + altitude.

Orbits | What do Kepler's laws say?

1: Orbits are ellipses with the central body at one focus. 2: Equal areas are swept out in equal times, so motion is faster nearer the central body. 3: T²/r³ is constant for circular orbits around the same body.

Orbits | How do geostationary and polar orbits differ?

Geostationary: circular, above the equator, eastward, with Earth's rotation period, so it stays over one place. Polar: passes over the poles while Earth turns below, allowing coverage of different regions.

Relativity | What is an inertial frame, and what are the two postulates?

An inertial frame is not accelerating. Physics has the same laws in every inertial frame, and all inertial observers measure the same vacuum light speed c, regardless of source motion.

Relativity | What is the Lorentz factor?

γ = 1/√(1 − v²/c²). It is at least 1 and grows as relative speed approaches c. At everyday speeds, γ is approximately 1.

Relativity | What is proper time, and what is time dilation?

Proper time Δt₀ is measured where the two events occur at the same position, such as a particle's birth and decay in its rest frame. Another inertial frame measures Δt = γΔt₀, a longer interval.

Relativity | What is proper length, and what is length contraction?

Proper length L₀ is measured with the object at rest. An observer moving relative to it measures L = L₀/γ along the motion, using simultaneous endpoint positions in that observer's frame. Perpendicular lengths do not contract.

Relativity | Why can an object with mass not reach light speed?

Relativistic momentum is p = γm₀v. As v approaches c, γ and the required energy grow without bound. A finite energy supply cannot accelerate a massive object to c.