Vectors, Units and prefixes

SI base units are:

Metres (m)

Seconds (s)

Moles (mol.)

Kilograms (kg)

Amperes (A)

Kelvin (K)

Derived quantities and units:

Formula

Derived unit

Unit

Speed= Distance/Time

Ms-1

Acceleration= velocity/time

Ms-2

Force =mass X acceleration

Kgms-2

Newtons

Pressure = force/area

Kgm-1s-1

Pascals

Work done (energy transfer)= force X distance

Kgm2s-2

Joules

Power = work done/time

Kgm2s-3

Watts

Charge= current x time

As

Coulombs

Potential difference = work done/charge

Kgm2s-3A-1

Volts

Resistance = potential difference/ current

Kgm2s-3A-2

Ohms

A physical quantity is something that can be measured.

A scalar has magnitude

A vector has magnitude and direction

A resultant vector of a horizontal and vertical component can either be found by calculation (Pythagoras and trigonometry) or by scale drawing and measurement.

When combining vectors, if one of them is subtracted, then reverse the direction.

You can find the separate vector components by using trigonometry to find the vertical and horizontal components.

Prefixes:

Prefix

symbol multiple Pico p 10-12

Nano

n

10-9

Micro μ 10-6

Milli

m

10-3

Centi c 10-2 kilo k

103

Mega

M

106 giga G

109

Terra

T

1012

Velocity= Δdisplacement/Δtime

Velocity is the rate of change of displacement.

Instantaneous velocity: δV/ δt

Acceleration= Δvelocity/Δtime

Acceleration is rate of change of velocity. a=(v-u)/t Projectiles and SUVAT equations

Velocity is rate of change of distance

Acceleration is rate of change of velocity

The SUVAT equations for motion are:

Gravitational acceleration can be calculated using a setup of an electromagnet which releases a steel ball and a hinged flap which detects when it drops, at a set distance and connected to a digital timer this can be used to obtain a value for g.

An object is in free-fall when it accelerates at g

Projectile motion – the motion of something that is travelling both horizontally and vertically.

Trajectory- the predicted path of a moving object.

There are 2 components of motion on a projectile: Vertical and horizontal. These are independent of each other, so horizontal and vertical speeds are independent.

In type 1 projectile motion questions you are required to resolve initial velocity into vertical and horizontal velocity and use these values in SUVAT equations.

In type 2 projectile motion questions you are required to resolve the initial velocity into vertical and horizontal components, then calculate the total time taken by the vertical component, and use this to calculate total distance horizontally.

The projected path and the actual path of a projectile differ because of air resistance causing it to decelerate in the horizontal component also. (Theoretically horizontal motion remains constant):

Newton’s Law’s

The centre of mass of an object is the point through which all of the mass of an object appears to be concentrated at.

The centre of gravity is the point at which the weight of an object appears to be concentrated at.

COM and COG are usually the same, objects balance at this point. The lower the COG is the more stable the object is, as an object will topple over when the COG is not over the base.

Newton’s First Law: the law of inertia

If a body has a number of forces acting on it, it will remain in a state of constant velocity if the sum of all the forces is zero.

This is called being in a state of equilibrium, and it means that the sums of components of forces in opposite directions are balanced, and the overall resultant force on the object is zero.

Remember: stationary is still a constant velocity, so if something is stationary it is in equilibrium.

The reaction force to weight is always perpendicular to the surface that an object is resting on.

The gravitational force between two objects depends on their masses and separation, and acts over distance. The force of attraction is only large when one or both masses are very large.

Tension is the state of an object subjected to a