INTRODUCTION TO PHYSICS

1.3 Understanding scalar and vector quantities

SCALAR QUANTITIES

Physical quantities that have magnitude only.

Example: length, time, temperature, mass, speed, area, volume and density.

VECTOR QUANTITIES

Physical quantities that have magnitude and direction

Example: displacement, momentum, acceleration, velocity and force.

INTRODUCTION TO PHYSICS

1.4 Understanding measurement

•The ability of the instrument to measure a quantity with little or no deviation among measurements.

Precision

•How close the measurement made is to the actual value. Accuracy

•Ability of instrument to detect change.

Sensitivity

RANDOM ERRORS

SYSTEMATICS ERRORS

ERROR IN MEASURE

MENT

SYSTEMATIC ERROR

•Due to the calibration of instrument.•Zero error- due to non-zero reading when actual reading should be zero.

RANDOM

ERROR

•Due to mistakes made when making measurement either through incorrect positioning of eye or instrument.•May also occur when there is a sudden change of environmental factors like temperature , air circulation or lighting.

ERROR IN MEASUREMENT

RANDOM ERRORS

PARALLAX ERRORS

SYSTEMATIC ERRORS

ZERO ERRORS

ErrorError is the difference between the actual value of a quantity and the value obtained in measurement.

There are 2 main types of error- Systematic Error- Random Error

Systematic ErrorSystematic errors are errors which tend to shift all measurements in a systematic way so their mean value is displaced. Systematic errors can be compensated if the errors are known.

Examples of systematic errors are zero error, which cause by an incorrect position of the zero point, an incorrect calibration of the measuring instrument. consistently improper use of equipment.

Systematic error can be reduced by Conducting the experiment with care. Repeating the experiment by using different instruments.

Zero error1. A zero error arises when the measuring instrument does not start from exactly zero.2. Zero errors are consistently present in every reading of a measurement.3. The zero error can be positive or negative.

NO ZERO ERROR: The pointer of the ammeter place on zero when no current flow through it.)

NEGATIVE ZERO ERROR: The pointer of the ammeter does not place on zero but a negative value when no current flow through it.)

(POSITIVE ZERO ERROR: The pointer of the ammeter does not place on zero but a negative value when no current flow through it.)

Random errors1. Random errors arise from unknown and unpredictable variations in condition.2. It fluctuates from one measurement to the next.3. Random errors are caused by factors that are beyond the control of the observers.4. Random error can cause by personal errors such as

human limitations of sight and touch.lack of sensitivity of the instrument: the instrument fail to

respond to the small change.natural errors such as changes in temperature or wind,

while the experiment is in progress.wrong technique of measurement.

5. One example of random error is the parallax error.

Random error can be reduced by- taking repeat readings- find the average value of the reading.

Parallax errorA parallax error is an error in reading an instrument due to the eye of the observer and pointer are not in a line perpendicular to the plane of the scale.

Precision1. Precision is the ability of an instrument in measuring a quantity in a consistent manner with only a small relative deviation between readings.2. The precision of a reading can be indicated by its relative deviation.3. The relative deviation is the percentage of mean deviation for a set of measurements and it is defined by the following formula:

Accuracy1. The accuracy of a measurement is the approximation of the measurement to the actual value for a certain quantity of Physics.2. The measurement is more accurate if its number of significant figures increases.3. Table above shows that the micrometer screw gauge is more accurate than the other measuring instruments.

4. The accuracy of a measurement can be increased by•taking a number of repeat readings to calculate the mean value of the reading.•avoiding the end errors or zero errors.•taking into account the zero and parallax errors.•using more sensitive equipment such as a vernier caliper to replace a ruler.5. The difference between precision and accuracy can be shown by the spread of shooting of a target (as shown in Diagram below).

Sensitivity1. The sensitivity of an instrument is its ability to detect small changes in the quantity that is being measured.2. Thus, a sensitive instrument can quickly detect a small change in measurement.3. Measuring instruments that have smaller scale parts are more sensitive.4. Sensitive instruments need not necessarily be accurate.