VECTORS, SCALARS AND VECTOR

ADDITIONYEAR 12

UNIT 1

MODULE 1

LESSON 2

As physicists, when do we and don’t we need to know about direction?

Discuss – in pairs or 3’s.

• Lesson Objective: To learn the difference between scalars and vectors and be able to categorise physical quantities as one or the other.

• 1.1.2 Scalars and vectors

• Define scalar and vector quantities and give examples.

• Draw and use a vector triangle to determine the resultant of two coplanar vectors such as displacement, velocity and force.

• Calculate the resultant of two perpendicular vectors such as displacement, velocity and force.

• Resolve a vector such as displacement, velocity and force into two perpendicular components.

ADMIN STUFF

• Nick.mason@oasisenfield.org – email me if you need anything. Or come see me – I’m mostly in C5

• www.physics-oasis.com – Timetable, Exam questions, Presentations etc.

• Homework will be set at least once a week – probably on Friday this week.

CONVERTING UNITS OF AREA AND VOLUME

10,000cm21m =100 cm

1m= 100 cm

1m2 = 10,000cm2 = 104cm2

1 cm2 = 1/104 m2= 10-4m2

1 m is 100cm,However 1m2 is 10000cm2 – Why?

Each side must be converted to centimetres before finding the area.

1000 000mm21m =1000 mm

1m= 1000 mm

1m2 = 1 000 000mm2= 106mm2

1mm2 = 1/ 106 m2 = 10-6m2

1m =100 cm

1m= 100 cm

1m3 = 1 000 000cm3 = 106cm3

1 cm3 = 1/106 m2= 10-6m2

100 00 00cm3

1m= 100 cm

1m =1000 mm

1m= 1000 mm

1m3 = 1 000 000 000mm3= 109mm3

1mm3 = 1/ 109 m3 = 10-9m3

1000 000 000mm 3

1m =1000 mm

QUESTION

? mm 35m3

1m3

1m3

Find the volume of the cuboid in mm3

SUMMARY1m 100cm 1000mm1m2 100cm x100 cm =

10,000cm2= 104cm2

1000mm x 1000mm=1,000 000 m2 =106

m2

1m3 100cm x 100cm x 100cm=1,000,000 cm3

= 106 cm3

1000 mm x 1000mm x 1000 mm= 1000000000 mm3

= 109 mm3

1mm 0.001m =10-3m

1mm2 10-6m2

1mm3 10-9m3

PREFIXES REVISITED

JUST FOR FUN… How big would all the world’s data be? http://

www.businessinsider.com/infographic-how-big-would-all-the-worlds-data-be-2012-8

Short answer: about 10 ZettaBytes

SCALARS AND VECTORS

Scalar: A quantity that is defined only by a magnitude

Vector: A quantity that has both direction and magnitude

Sort the following physical quantities into scalars and vectors:

Velocity, Force, Speed, Distance, Displacement, Acceleration, Kinetic Energy, Gravitational Potential Energy, Weight, Potential Difference (Voltage), Time, Electric Current, Electric Charge.

Extension: If you are familiar with them, try adding these quantities: Electric Field, Wavelength, Frequency.

Extension 2: Add any quantities of your own, that I have missed off.

When two or more vectors are added the resulting sum of the vectors is called the RESULTANT vector or simply the RESULTANT.

This could be a resultant velocity, force, acceleration etc. depending on the nature of the original vectors.

Vector addition

(i) vectors acting in the same lineTwo or more vectors acting in the same direction may be added as if they were scalars. For example the sum, or resultant of the three forces shown in Fig. 1(a) is 50 N acting right to left while in (b) it is 250 N left to right

Vectors acting in the same line

But what if they’re not in the same line?