Physics • Year 12 • Module 5 • Lesson 7
Uniform Circular Motion
Lock in the core vocabulary, the key formulas, and the conceptual distinctions between speed, velocity, and acceleration in circular motion before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: period, frequency, angular velocity, linear speed, centripetal acceleration, centripetal force, uniform circular motion, tangential velocity. 8 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The time required for one complete revolution of an object moving in a circle. Symbol T, unit: seconds (s). | |
| 1.2 | The number of complete revolutions per second. Symbol f, unit: hertz (Hz). Equals 1/T. | |
| 1.3 | The rate at which the angular position changes, equal to 2π/T or 2πf. Symbol ω, unit: rad/s. | |
| 1.4 | The distance travelled per unit time along the circular path. Equal to ωr or 2πr/T. Unit: m/s. | |
| 1.5 | The acceleration directed toward the centre of the circular path, equal to v²/r or ω²r. Unit: m s−². | |
| 1.6 | The net force directed toward the centre required to maintain circular motion. Not a new type of force. Equal to mv²/r. | |
| 1.7 | Motion in a circle at constant speed; velocity is not constant because direction continuously changes. | |
| 1.8 | The instantaneous velocity vector of a circularly moving object; always directed tangent to the circle at the object’s position. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 In uniform circular motion, the speed of the object is constant and therefore the acceleration is zero. T / F
2.2 The centripetal force is a separate, special force that appears whenever an object moves in a circle. T / F
2.3 If the radius of a circular path doubles and speed stays the same, the centripetal force halves. T / F
2.4 For an object in uniform circular motion, centripetal acceleration points toward the centre and is perpendicular to the velocity. T / F
2.5 The relationship between angular velocity and frequency is ω = f/2π. T / F
2.6 If the centripetal force on a whirling ball is suddenly removed, the ball will fly outward in the radial direction. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
centripetal · direction · friction · inertia · net · perpendicular · speed · velocity
In uniform circular motion the ___________ of an object is constant, but its ___________ changes continuously because the ___________ of motion changes at every point on the path. A change in velocity means there is acceleration, called ___________ acceleration, which always points toward the centre of the circle. By Newton’s Second Law, this acceleration requires a ___________ inward force. This force is always ___________ to the object’s velocity vector, so it does no work on the object. On a flat road, the centripetal force for a turning car is provided by ___________ from the tyres. If that force disappears, the object continues in a straight line due to ___________, not because of any outward force.
4. Formula recall card
Complete the table. For each formula, fill in the name of each variable, its SI unit in brackets, and a one-line description of when to use the formula. 10 marks (2 per row)
| Formula | Variable meanings & SI units | When to use it |
|---|---|---|
| v = ωr | v = (____); ω = (____); r = (____) | |
| ac = v²/r | ac = (____); v = (____); r = (____) | |
| Fc = mv²/r | Fc = (____); m = (____); v, r as above | |
| ω = 2πf = 2π/T | ω = (____); f = (____); T = (____) | |
| v = 2πr/T | v = (____); r = (____); T = (____) |
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “is provided by”, “requires”, “equals”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: centripetal acceleration · centripetal force · velocity (vector) · net inward force · angular velocity · linear speed.
Q1 — Term–definition match
1.1 period • 1.2 frequency • 1.3 angular velocity • 1.4 linear speed • 1.5 centripetal acceleration • 1.6 centripetal force • 1.7 uniform circular motion • 1.8 tangential velocity
Q2 — True / false with correction
2.1 False. Speed is constant but velocity is not, because the direction of motion continuously changes. A changing velocity means there is acceleration (— the centripetal acceleration, directed toward the centre). Acceleration is not zero.
2.2 False. Centripetal force is not a new type of force. It is the name given to the net inward force that maintains circular motion. This force can be provided by tension, friction, gravity, or the normal force depending on the situation.
2.3 True. Since Fc = mv²/r, if r doubles and v is constant, Fc = mv²/(2r) — the force halves.
2.4 True. Centripetal acceleration always points toward the centre, and the velocity is always tangent to the circle. Radial and tangential directions are perpendicular; hence acceleration is perpendicular to velocity.
2.5 False. The correct relationship is ω = 2πf (not f/2π). Angular velocity is 2π radians per revolution, so ω = 2π × (revolutions per second) = 2πf.
2.6 False. If the centripetal force is removed, the ball travels in a straight line tangent to the circle (Newton’s First Law). It does not fly radially outward — there is no outward force. The apparent outward motion is because the ball no longer follows the curved path.
Q3 — Cloze paragraph
In order: speed / velocity / direction / centripetal / net / perpendicular / friction / inertia.
Q4 — Formula recall card (sample answers)
v = ωr: v = linear (tangential) speed (m s−1); ω = angular velocity (rad/s); r = radius (m). Use when converting between angular and linear quantities.
ac = v²/r: ac = centripetal acceleration (m s−2); v = linear speed (m s−1); r = radius (m). Use when you know speed and radius and need the acceleration toward the centre.
Fc = mv²/r: Fc = centripetal (net inward) force (N); m = mass (kg); v, r as above. Use when you need the net inward force required for circular motion.
ω = 2πf = 2π/T: ω = angular velocity (rad/s); f = frequency (Hz); T = period (s). Use when converting frequency or period to angular velocity.
v = 2πr/T: v = linear speed (m s−1); r = radius (m); T = period (s). Use when period and radius are known and linear speed is required.
Q5 — Sample concept map arrows
- centripetal force — equals the → net inward force
- centripetal acceleration — requires, by Newton’s 2nd Law, → centripetal force
- angular velocity — multiplied by radius gives → linear speed
- linear speed — squared and divided by r gives → centripetal acceleration
- centripetal acceleration — continuously changes the direction of → velocity (vector)
- angular velocity — multiplied by r gives the magnitude of → velocity (vector)
Award 1 mark per valid labelled arrow (minimum 6, maximum 6 marked). Accept any scientifically correct linking phrases.