1.2 Advanced Motion
Circular Motion & Terminal Velocity
🎯 The Hook
Satellites orbit Earth at thousands of km/h yet never fall down. Skydivers accelerate at first, then reach a constant speed. Both phenomena involve forces that DON'T change speed the way you'd expect.
💡 The Why
Understanding circular motion explains how satellites, planets, and even atoms work. Terminal velocity is crucial for parachute design, vehicle safety, and understanding drag forces in engineering.
Part 1: Circular Motion
Baby Steps (Plain English)
- Imagine swinging a ball on a string in a circle above your head
- The ball moves at constant speed, but its direction keeps changing
- Since velocity = speed + direction, the velocity is constantly changing
- Change in velocity means there's acceleration
- The string pulls the ball inward, providing the force for this acceleration
Interactive Orbital Simulation
Watch how velocity (green) is always tangent to the circle, while force (red) points inward
🔑 Deep Theory (Mark Scheme Keywords)
Speed: The magnitude of velocity. In circular motion, speed remains constant.
Velocity: Speed in a stated direction. In circular motion, velocity is constantly changing because direction changes.
Acceleration: Rate of change of velocity. In circular motion, there is acceleration toward the center (centripetal acceleration) even though speed is constant.
Centripetal Force: The force directed toward the center that keeps an object moving in a circle. This force does NOT increase the object's speed; it only changes its direction.
Critical Concept: The force is perpendicular (90°) to the velocity vector. A perpendicular force changes direction but not speed.
⚠️ Examiner's Trap
- Trap: "Speed is constant so there is no acceleration" WRONG! Velocity changes so there IS acceleration.
- Trap: "The satellite is weightless" WRONG! Gravity provides the centripetal force.
- Mark Scheme: Always state that velocity is changing even when speed is constant because DIRECTION is changing.
- Common Error: Confusing speed (scalar) with velocity (vector). Only vectors can have direction.
Part 2: Terminal Velocity
Baby Steps (Plain English)
- A skydiver jumps from a plane. Initially, only weight acts downward
- As they fall faster, air resistance increases (faster speed = more air resistance)
- Weight stays constant but air resistance keeps growing
- Eventually, air resistance equals weight (balanced forces)
- When forces balance, net force = 0, so acceleration = 0
- The skydiver continues falling at constant speed (terminal velocity)
Interactive Terminal Velocity Simulator
Force Diagram
Speed-Time Graph
Watch the speed curve flatten as air resistance increases to match weight
🔑 Deep Theory (Mark Scheme Keywords)
Weight: The gravitational force acting on an object. Weight = mg. This force is constant and always acts downward.
Air Resistance (Drag): A frictional force that opposes motion through air. Air resistance increases with speed.
Terminal Velocity: The constant maximum speed reached when the upward air resistance equals the downward weight, resulting in zero net force and zero acceleration.
The Process: Initially Weight greater than Air Resistance leads to Net Force Downward leads to Acceleration Downward leads to Speed Increases leads to Air Resistance Increases leads to Eventually Air Resistance = Weight leads to Net Force = 0 leads to Acceleration = 0 leads to Constant Speed (Terminal Velocity)
⚠️ Examiner's Trap
- Trap: "At terminal velocity, there is no force" WRONG! Forces are balanced (Weight = Air Resistance) but both still act.
- Trap: "Weight decreases as you fall" WRONG! Weight is constant (mg does not change). Only air resistance changes.
- Mark Scheme: Must state "resultant force becomes zero" or "net force is zero" NOT just "no force".
- Common Error: Saying velocity is zero at terminal velocity. Terminal velocity is constant, NOT zero!
- Graph Trap: Speed-time graph should curve and flatten, NOT form a triangle.
📋 Syllabus Coverage Checklist (Extended)
💪 Quick Revision Points
- Circular motion: Speed constant, velocity changing, acceleration present
- Centripetal force points to center, perpendicular to velocity
- Terminal velocity: Air resistance = Weight means Net force = 0
- At terminal velocity: No acceleration, but forces still act (balanced)
- Speed-time graph for falling: Starts steep, curves, then flattens
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