Vectors and Scalars Scalars are quantities which have
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Vectors and Scalars • Scalars are quantities which have magnitude only • Vectors have both magnitude and direction • To identify a vector fully you must give both its magnitude and its direction
Scalars • • distance mass temperature speed Time charge volume Vectors • • • displacement force velocity acceleration magnetic field strength • weight
40 N
30 N
30 N 40 N
30 N 50 N 40 N
20 N
20 N
Adding Vectors • • Draw the vectors to scale. Place the vectors nose to tail. Draw a line in to complete the triangle. The length of the new line is the sum of the vectors. • It is also possible to add vector quantities algebraically. We will do this in easy cases.
The vector parallelogram
Adding Vectors • Because of the parallelogram rule it doesn’t really matter if the tails of the vectors are put together. You will still get the same diagonal. • This is often more convenient. (Mathematicians call it using based vectors)
The vector parallelogram
Using Mathematics • You will be expected to be able to add two vectors which are at right angles using the Pythagoras theorem.
Example A rowing boat is rowed 12 metres across a fast stream towards a point on the bank directly opposite. The current carries the boat 8 metres at right angles to this. What is the total distance travelled by the boat 8 m 12 m
Example A rowing boat is rowed 12 metres across a fast stream towards a point on the bank directly opposite. The current carries the boat 8 metres at right angles to this. What is the total distance travelled by the boat 8 m 12 m
Example A rowing boat is rowed 12 metres across a fast stream towards a point on the bank directly opposite. The current carries the boat 8 metres at right angles to this. What is the total distance travelled by the boat 8 m 12 m
A rowing boat is rowed 12 metres across a fast stream towards a point on the bank directly opposite. The current carries the boat 8 metres at right angles to this. What is the total distance travelled by the boat 8 m 12 m