Ch 8 · 1.5.4 Circular Motion · O Level Physics 5054

Topic 8 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 49 lessons.

Introduction

Swing a ball on a string in a circle, then let go: it flies off in a straight line. So what kept it going round? Circular motion needs a force, even when the speed never changes. This lesson explains that force qualitatively: no formula is needed at O Level. (Syllabus section 1.5.4.)

Key ideas — Why a force is needed

An object moving in a circle at constant speed is continually changing direction, so its velocity is changing. By Newton's first law, a change in velocity needs a resultant force.

🧑‍🏫 Teacher's explanation

Imagine you are swinging a ball on a string around your head. The ball wants to fly off in a straight line because of its inertia, but the string pulls it inward toward your hand. This pull is a force acting at a right angle (perpendicular) to the direction the ball is moving.

📖 Definitions

🔍 Worked example — Easy

A toy car moves in a circle at a constant speed of 5 m/s. Does the car have a resultant force acting on it? Explain why.

🔍 Worked example — Standard

A stone is whirled on a string in a circle. If the speed of the stone is kept constant, but the strength of the pull on the string (the force) is doubled, what happens to the radius of the circular path?

🔍 Worked example — Exam-style

A car of mass m travels around a circular bend at a constant speed. A second car of mass 2m travels around a bend of the same radius at the same speed. Compare the force required for the second car to the first car.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Explain why there must be a resultant force acting on the mass. [2] (b) If the speed of the mass is kept constant but the mass of the object is doubled, describe and explain the change in the force required to maintain the same circular path. [2] [4 marks]

Key ideas — Direction of the force

The force acts perpendicular (at right angles) to the motion, towards the centre of the circle. It changes the direction of motion but not the speed.

🧑‍🏫 Teacher's explanation

Imagine you are swinging a ball on a string in a circle above your head. The ball wants to fly off in a straight line due to its inertia, but the string pulls it constantly toward your hand. This pull is always at a right angle to the direction the ball is moving. Because the pull is sideways relative to the motion, it doesn't speed the ball up or slow it down; it only 'steers' it, changing its direction to keep it in a circle.

📖 Definitions

🔍 Worked example — Easy

A small stone is whirled in a horizontal circle on a string. If the speed of the stone is constant, what is the direction of the force acting on the stone relative to its velocity?

🔍 Worked example — Standard

A car is traveling around a circular bend of radius r at a constant speed v. If the driver wants to maintain the same speed and radius but the car's mass is doubled, how must the required centripetal force change?

🔍 Worked example — Exam-style

A satellite orbits a planet in a circular path. If the orbital speed is kept constant but the orbital radius is decreased by half, what happens to the required centripetal force?

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Where the force comes from

If the force disappears (the string breaks, the road is icy), the object carries on in a straight line at a tangent to the circle.

🧑‍🏫 Teacher's explanation

Imagine you are swinging a bucket of water in a vertical circle. Even though the bucket wants to fly off in a straight line, the string pulls it back toward your hand. This pull is always at a right angle (perpendicular) to the direction the bucket is moving. This constant 'tug' towards the center is what forces the object to turn rather than traveling in a straight line.

📖 Definitions

🔍 Worked example — Easy

A car travels around a circular bend. If the friction between the tyres and the road increases while the car's speed and the radius of the bend remain constant, what happens to the motion?

🔍 Worked example — Standard

A satellite orbits a planet in a circular path. If the mass of the satellite is doubled, but we want it to maintain the exact same orbital speed and the same orbital radius, how must the gravitational force change?

🔍 Worked example — Exam-style

A stone is whirled on a string in a circle of radius r. If the string is suddenly cut, describe the path of the stone.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — How the force depends on speed, radius and mass

(The equation F = mv^2/r is not required for 5054.)

🧑‍🏫 Teacher's explanation

Imagine you are swinging a ball on a string in a circle above your head. The string provides a force that pulls the ball toward your hand. This force is always perpendicular to the direction the ball is moving; if it weren't, the ball would move in a straight line rather than a circle.

📖 Definitions

🔍 Worked example — Easy

A small stone is being whirled on a string in a horizontal circle. If the speed of the stone is doubled while the mass of the stone and the radius of the circle remain constant, what happens to the required force?

🔍 Worked example — Standard

A car travels around a circular bend of radius r at a constant speed. If the driver wants to take a tighter turn (a smaller radius) while maintaining the same speed, what must happen to the friction force between the tires and the road?

🔍 Worked example — Exam-style

Two objects, A and B, are moving in identical circular paths (same radius) at the same speed. Object A has a mass of 2.0 kg and Object B has a mass of 10 kg. How does the force required for Object B compare to the force required for Object A?

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) State the effect on the required force if the speed of the object is increased, while its mass and the radius of the path remain constant. [1] (b) A second object of greater mass is moving in a circle of the same radius and at the same speed as the first object. Describe the change in the force required to maintain this motion. [1] [2 marks]

Worked example

Example: a car on a bend. A car goes round a bend at constant speed.

🔍 Worked example — Easy

A car travels around a circular bend at a constant speed. Explain why there must be a resultant force acting on the car.

🔍 Worked example — Standard

A car is driving around a circular track. If the mass of the car and the radius of the track remain constant, what happens to the speed if the friction between the tires and the road is doubled?

🔍 Worked example — Exam-style

A heavy truck and a small car are both traveling around a bend of the same radius at the same speed. Which vehicle requires a greater force to stay on the bend, and why?

⚠️ Common errors

Common mistakes

Practice

Answers: (1) Its direction, and so its velocity, is continually changing; this needs a resultant force towards the centre (gravity). (2) Friction between the tyres and the road, towards the centre. (3) The tension must increase. (4) A larger force is needed.

Ch 8 · 1.5.4 Circular Motion · O Level Physics 5054

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