OxfordAQA International GCSE Physics: Terminal velocity, centre of mass, moments and levers (9203) – Revision Notes

These notes condense sections 3.1.6 to 3.1.8 of the OxfordAQA International GCSE Physics (9203) specification, version 5.2, for exams May/June 2018 onwards. Full explanations and worked examples are in the study guide. Test yourself with the practice questions, tick topics off on the checklist, and find the rest of the course on the OxfordAQA Physics hub. The wider topic notes are Forces and Their Effects revision notes. For a quick check of weak spots, use the free diagnostics.

Key definitions

Term	Meaning
Drag	Frictional force on an object moving through a fluid; opposes motion; grows as speed grows
Fluid	A liquid or a gas
Terminal velocity	The constant velocity reached when the resultant force is zero, so drag equals the driving force (weight, for a falling object)
Streamlining	Shaping an object so fluid flows smoothly past, reducing drag
Centre of mass	The point at which the mass of an object may be thought to be concentrated
Moment	The turning effect of a force
Principle of moments	For an object that is not turning, total clockwise moment = total anticlockwise moment about any pivot
Force multiplier	A lever or tool in which a small effort overcomes a larger load

Formulas

Quantity	Equation	Units
Moment	M = F × d	N m, N, m (d is the perpendicular distance from the pivot)
Weight	W = m × g	N, kg, N/kg
Resultant force	F = m × a	N, kg, m/s²
Acceleration from a graph	gradient of a velocity-time graph	m/s²

Values of g used here are quoted as 10 N/kg. In an exam, use the value given in the question.

Terminal velocity in steps

1. Start: speed zero, drag zero, resultant = weight, acceleration largest.
2. Speed rises, drag rises, resultant falls, acceleration falls.
3. Drag = weight, resultant zero, acceleration zero: constant speed.

Always write “the resultant force is zero”, not “there are no forces”.

Velocity-time graph with a parachute

Stage	Graph	Forces
Free fall	Steep line that curves over	Weight > drag
Terminal velocity 1	Flat, high	Weight = drag
Parachute opens	Sharp fall in speed	Drag > weight
Terminal velocity 2	Flat, low	Weight = drag

Rough shape, with time across and speed up:

speed
 |      ________
 |    /         \
 |  /            \
 | /              \________
 |/___________________________ time

• The gradient gives the acceleration.
• The speed after the parachute has opened settles at a lower value because the parachute increases drag at any given speed.
• At both flat sections, drag equals the same weight. The parachute does not change the weight.

Why parachutes work

The large area gives a large drag at low speed. A bigger drag force means the weight is balanced at a lower speed, so the terminal velocity is lower and the landing is safer.

Streamlining

Object	Streamlined features	Effect
Shark (an adaptation)	Smooth, tapered body and smooth skin	Water flows smoothly, drag falls, swims faster with less energy
Car (a design feature)	Smooth curved body, sloping bonnet and windscreen, low front	Air flows smoothly, drag falls, higher maximum speed

Structure of a good answer: shape, then smooth flow, then less drag, then the benefit.

Centre of mass

• The weight of an object can be treated as acting at its centre of mass.
• A symmetrical object has its centre of mass on the axis of symmetry.
• A freely suspended object rests with its centre of mass directly below the pivot.
• The centre of mass can be outside the object (a ring, for example).

Method: irregular thin lamina

1. Make three holes near the edge.
2. Hang the lamina on a pin so it swings freely.
3. Hang a plumb line from the pin and mark two points along it.
4. Remove the lamina and draw the line.
5. Repeat for two other holes. The lines cross at the centre of mass.

Sources of error: pin held too tightly, plumb line moving when marked, marks too close together.

Stability

Low centre of mass and wide base mean more stable. High centre of mass and narrow base mean easier to topple.

Moments

M = F × d. Always check three things: the force is the one acting on the object, d is perpendicular to the line of action, and the units match (convert cm to m).

Method for balanced objects

1. Pick a pivot (often the support).
2. List clockwise moments and anticlockwise moments.
3. Set the totals equal.
4. Solve for the unknown force or distance.

Quick reminder 1. A 450 N force acts 0.20 m from a pivot. The moment is 450 × 0.20 = 90 N m.

Quick reminder 2. A 240 N weight sits 0.75 m left of a pivot. A force F sits 0.50 m right of it. Balance: F × 0.50 = 240 × 0.75 = 180, so F = 360 N.

Quick reminder 3. A uniform plank has its weight at its middle. If the pivot is at the middle, the plank’s own weight has no moment and can be ignored. If the pivot is elsewhere, include the plank’s weight at its centre.

The support force at a pivot equals the sum of the downward forces when the object is in equilibrium.

Toppling

• The weight acts down through the centre of mass.
• If the line of action of the weight is inside the base, the object returns upright when tilted.
• If it is outside the base, there is a resultant moment about the tipping edge and the object topples.
• Vehicles: a high load raises the centre of mass, so a smaller tilt takes the line outside the wheels.
• Balancing toys: the weighted arms put the centre of mass below the pivot, so the weight turns the toy back when it is nudged.

For a push on a box: tipping starts when push moment about the lower edge equals weight moment about the same edge.

Levers

A simple lever is a bar that turns about a pivot. Effort × distance from pivot (effort) = load × distance from pivot (load) at balance. Effort far from the pivot and load close to it gives a force multiplier.

Quantity	Value
Force multiplier	load ÷ effort = effort distance ÷ load distance
Cost	The effort moves further than the load

Examples: crowbar, wheelbarrow, nutcracker.

Quick self-test

1. State what happens to drag as the speed of an object in a fluid increases.
2. A skydiver of mass 70 kg experiences a drag of 280 N at one instant. Find the acceleration.
3. State the resultant force on a skydiver at terminal velocity.
4. Explain why a skydiver slows down when the parachute opens.
5. Give two features of a shark that reduce drag.
6. Describe where the centre of mass of a rectangular sheet is.
7. Calculate the moment of 35 N acting at 0.60 m from a pivot.
8. A force of 90 N acts 0.40 m from a pivot. What force at 0.12 m gives the same moment?
9. A beam balances with 120 N at 0.50 m on the left. What force at 0.80 m on the right balances it?
10. State when an object will topple.
11. A lever has an effort of 40 N at 0.90 m from the pivot. The load is 0.15 m from the pivot. Find the load.

Answers

1. Drag increases.
2. Weight = 70 × 10 = 700 N. Resultant = 700 − 280 = 420 N. a = 420 ÷ 70 = 6.0 m/s².
3. Zero.
4. Drag becomes bigger than weight, so the resultant force acts upwards and the skydiver decelerates until drag again equals weight at a lower speed.
5. Smooth, tapered body; smooth skin (any two).
6. At the point where the axes of symmetry cross, the middle of the sheet.
7. 35 × 0.60 = 21 N m.
8. Moment = 90 × 0.40 = 36 N m. F = 36 ÷ 0.12 = 300 N.
9. Anticlockwise = 120 × 0.50 = 60 N m. F = 60 ÷ 0.80 = 75 N.
10. When the line of action of its weight lies outside its base.
11. Load = 40 × 0.90 ÷ 0.15 = 240 N.

Where marks are usually lost

• Writing “no resultant force” as “no force”.
• Saying the skydiver “stops accelerating” without linking this to drag equalling weight.
• Writing that a parachute “reduces gravity” or “reduces weight”.
• Using the distance along the bar when the force is not at right angles to it.
• Forgetting the unit N m, or using N/m.
• Leaving centimetres in a moment calculation.
• Describing a lamina method without a plumb line or without hanging from more than one point.
• Saying “streamlined” without explaining smooth flow and less drag.
• Explaining toppling with “too heavy” instead of the position of the line of action of the weight.

Official syllabus

These notes follow the OxfordAQA International GCSE Physics (9203) specification, version 5.2, for exams May/June 2018 onwards, published by OxfordAQA.