Scalars and vectors Cambridge International AS & A Level Physics revision
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In plain words
Some quantities are just a size: mass, energy, time. Others have a direction too: force, velocity, momentum. You can't add those like ordinary numbers. The trick that makes almost every vector problem easy is to split each one into two parts at right angles.
Three things to know
- A scalar has magnitude only. A vector has magnitude and direction. Displacement, velocity, acceleration, force and momentum are vectors.
- Resolving: a vector F at angle θ to the horizontal has a horizontal component F cos θ and a vertical component F sin θ.
- To add vectors, draw them tip to tail; the resultant closes the triangle. For two at right angles, use Pythagoras for the size and tan for the angle. Three forces in equilibrium form a closed triangle.
Worked example
A force of 50 N acts at 30° above the horizontal. Find its components.
- Horizontal: 50 cos 30° = 43.3 N.
- Vertical: 50 sin 30° = 25.0 N.
- Check: √(43.3² + 25.0²) = 50 N.
Tips and tricks
- The component next to the angle uses cos; the one opposite uses sin.
- Resolve along the directions that suit the problem: on a slope, parallel and perpendicular to the slope.
It lands in your notebook with its questions as flashcards.
Scalars and vectors: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Which of these is a vector?
Momentum has the direction of the velocity.
A 100 N force acts at 30° to the horizontal. What is its vertical component?
100 sin 30°.
Forces of 3 N and 4 N act at right angles. What is the resultant?
√(9 + 16).
Which could not be the resultant of a 5 N force and a 7 N force?
The resultant lies between 7 − 5 = 2 N and 7 + 5 = 12 N.
Three forces act on a body in equilibrium. What shape do they make when drawn tip to tail?
A closed shape means the resultant is zero.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Scalars and vectors
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
Forces of 6.0 N and 8.0 N act at right angles. Find the magnitude of the resultant and its angle to the 6.0 N force.[3]
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10 N, at 53° to the 6.0 N force. tan⁻¹(8.0 ÷ 6.0).
A ball leaves the ground at 20 m/s at 60° to the horizontal. Find the horizontal component of its velocity.[2]
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10 m/s. 20 cos 60°.
A block of weight W rests on a slope at angle θ to the horizontal. Write down the components of its weight along and at right angles to the slope.[2]
Show answerHide answer
W sin θ along the slope, and W cos θ at right angles to it.
Answers: Scalars and vectors
- 1. 10 N, at 53° to the 6.0 N force. tan⁻¹(8.0 ÷ 6.0).
- 2. 10 m/s. 20 cos 60°.
- 3. W sin θ along the slope, and W cos θ at right angles to it.