SCALARS AND VECTORS Scalars have MAGNITUDE ONLY Eg

SCALARS AND VECTORS Scalars have MAGNITUDE ONLY Eg distance, mass, speed Vectors have MAGNITUDE and DIRECTION Eg displacement, velocity, force, acceleration, momentum Vectors can be represented using bold print eg: F, v, a

SCALARS AND VECTORS Distance and Displacement B Distance AB = half circumference (pr) Displacement AB = 2 r (upwards) Distance A to A (one revolution) = 2 pr A Displacement A to A = zero Displacement is measured from the starting position

oscillates Mass on a spring x -x A Rest (equilibrium) position B Vectors have DIRECTION and can be positive or negative

VECTOR ADDITION 5 N 3 N gives a resultant = 2 N BUT: 5 N 3 N gives a resultant = 8 N

So how about this 5 N 25 deg 3 N To find the resultant (between 2 N and 8 N) we must do a scale diagram a) Choose a suitable (big) scale b) Draw ONE vector to scale eg 2 cm : 1 N 25 deg 10 cm c) Draw the other vector to scale in its direction but it MUST be top to tail d) Resultant joins up the two open ends, taken from the It has magnitude and direction SAME starting point 6 cm

If 2 vectors are at right angles: Draw or use pythagoras 3 N q 2 N R 2 = 3 2 + 2 2 q = tan-1(2/3)

RESOLUTION OF VECTORS Any vector can be replaced by 2 other vectors at right angles. But an infinite number of pairs: so it is usually done Vertically/horizontally, or parallel and perpendicular to a plane 5 N q x x/5 = cos q so x = 5 cos q y/5 = sin q so y = 5 sin q y

So you can resolve any vector into it’s two components quick as a flash!!! q v The 2 components are…… V cos q and V sin q The “cos” one is NEXT to the angle

Inclined plane Normal reaction R. Friction F 30 o Weight (= mg) Qu: If weight = 10 N, find the values of R and F Resolve weight into its two components parallel to, and perpendicular to the slope Right angle triangle What is the top angle? 30 o The 2 components: quick as a flash: 10 sin 30 and 10 cos 30 Must be equal and opposite to F and R Which is which?

Multiplying and dividing vector and scalar quantities Multiply a scalar and a eg : Force = mass x acceleration vector result: F = ma a VECTOR Multiply a vector and a vector result: eg Power = force x velocity a SCALAR P = FV Same rules for dividing

Relative velocities 3 ms-1 2 ms-1 Relative velocity of RED to BLUE = 6 ms-1 RIGHT Of BLUE to RED = 6 ms-1 LEFT

150 ms-1 200 ms-1 Relative velocity of blue to red? 150 ms-1 Rel 200 ms-1 150