Preview
IB DP Physics — Unit A: Space, Time and Motion | SL & HL | A.2 Forces and Momentum
📋 What You Will Learn
- Observe and describe the physical phenomenon of circular motion using real-world examples such as satellites, car cornering, and spinning objects
- Define angular displacement, angular velocity, period, frequency, and centripetal acceleration with correct units and notation
- Derive the expressions for centripetal acceleration and centripetal force from first principles using velocity vector analysis
- Apply Newton's second law to circular motion problems involving banked tracks, conical pendulums, and vertical circles
- Analyse force diagrams and free body diagrams for objects moving in horizontal and vertical circles
- Evaluate common misconceptions about centrifugal force and connect circular motion to gravitation, electromagnetism, and energy
🌍 Real-World Context When a car rounds a sharp bend on a motorway, the passengers feel pressed outward against the door. When a satellite orbits Earth, it travels at enormous speed yet never flies away into space — nor does it fall straight down. When a hammer-thrower spins before releasing the hammer, the athlete must pull inward with tremendous force to keep the hammer moving in a circle. In each of these situations, something is forcing an object to continuously change its direction of motion, even when its speed remains constant. This is the central puzzle of circular motion: how can an object be accelerating if its speed is not changing?
🔍 Guiding Question What force is required to keep an object moving in a circle, and how does it depend on the object's speed, mass, and the radius of the circular path?
Physical Setup and Diagram
Consider a small object — a ball on a string — being swung in a horizontal circle at constant speed. The ball traces out a circular path, returning to the same point after each complete revolution. Although the speed of the ball does not change, its direction of motion changes continuously: at every instant, the ball is heading in a different direction. This continuous change of direction is what makes circular motion fundamentally different from straight-line motion.
Notice from the top-view diagram that the velocity arrow is always tangent to the circle — it is always perpendicular to the radius at that point. As the ball moves around the circle, the direction of this velocity arrow rotates continuously. The centripetal acceleration arrow always points toward the centre of the circle, regardless of where the ball is on its path. This inward direction is the defining feature of circular motion.
Core Concepts and Definitions
Before we can write any equations, we need a way to describe how far around the circle an object has travelled. In linear motion, we use displacement in metres. In circular motion, it is more natural to describe position using the angle swept out from a reference direction. This angle is called the angular displacement, and it is measured in radians rather than degrees.
📖 Key Definition — Angular Displacement Angular displacement \( \theta \) is the angle, measured in radians, swept out by the radius as an object moves along a circular arc. One complete revolution corresponds to an angular displacement of \( 2\pi \) radians.
The relationship between the arc length \( s \) travelled along the circle and the angular displacement \( \theta \) is \( s = r\theta \), where \( r \) is the radius of the circle. This means that a larger radius produces a longer arc for the same angle swept. Here \( s \) is measured in metres (m), \( r \) in metres (m), and \( \theta \) in radians (rad).
📖 Key Definition — Angular Velocity Angular velocity \( \omega