INTRODUCTION TO PHYSICS Measurement, Significant Digits, Precision & Accuracy

KINEMATICS Position and Motion

Motion involves a change in the position of an object over time. Motion can be described using mathematical relationships. Many technologies that apply concepts related to kinematics have societal and environmental implications. BIG IDEAS IN KINEMATICS

DYNAMICS Forces and the Causes of Motion

Forces can change the motion of an object. Newton’s Three Laws of Motion that govern how forces change motion Applications of Newton’s laws of motion have led to technological developments that affect society and the environment. BIG IDEAS IN DYNAMICS

ENERGY Ability to Do Work

Energy can be transformed from one type to another. Energy transformations are never 100% efficient. Applications that involve energy transformations (e.g. power generation) can affect society and the environment in positive ways, but also have negative effects. BIG IDEAS IN ENERGY

ELECTRICITY AND MAGNETISM

WAVES & SOUND Behaviour of Waves and Properties of Sound

You throw a coin horizontally off the CN Tower at exactly the same time that your friend drops a coin. Compare the time in the air for both coins and their paths to the ground. GROUP LEARNING: PRACTICE QUESTION #1

You see a number of birds sitting contentedly on a horizontal electrical wire. You wonder why they do not experience an electric shock. GROUP LEARNING: PRACTICE QUESTION #2

Explain what happens to the pitch of a siren from an ambulance or fire truck as it approaches and then passes a stationary observer. GROUP LEARNING: PRACTICE QUESTION #3

In a collision between a mosquito and the windshield of a speeding SUV, compare the force that each exerts on the other. GROUP LEARNING: PRACTICE QUESTION #4

SIGNIFICANT DIGITS Limitation of Measurement

A JUSTIFICATION FOR “SIG DIGS” Measurements are not perfect.

They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision. A JUSTIFICATION FOR “SIG DIGS”

Measurements are not perfect. They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision. Note that we are not talking about human errors here.

PRECISION We indicate the precision to which we measured our quantity in how we write our measurement.

PRECISION We indicate the precision to which we measured our quantity in how we write our measurement. For example, which measurement is more precise?  15 cm  15.0 cm

PRECISION We indicate the precision to which we measured our quantity in how we write our measurement. For example, which measurement is more precise?  15 cm  15.0 cm  This one, obviously.

WHAT WE MEAN  When we write 15 cm, we mean that we’ve measured the quantity to be closer to 15 cm than to 14 cm or 16 cm BUT  When we write 15.0 cm, we mean that we’ve measured the quantity to be closer to 15 cm than to 14.9 cm or 15.1 cm.

SIGNIFICANCE Digits that have been measured are said to be significant.  15 cm  This measurement has 2.  15.0 cm  This measurement has 3.

THE FOLLOWING RULES ARE USED TO DETERMINE IF A DIGIT IS SIGNIFICANT:  All non-zero digits are significant e.g N has three significant digits

THE FOLLOWING RULES ARE USED TO DETERMINE IF A DIGIT IS SIGNIFICANT:  All non-zero digits are significant  Any zeroes placed after other digits and behind a decimal are significant e.g kg has three significant digits

THE FOLLOWING RULES ARE USED TO DETERMINE IF A DIGIT IS SIGNIFICANT:  All non-zero digits are significant  Any zeroes placed after other digits and behind a decimal are significant  Any zeroes placed between significant digits are significant e.g m has four significant digits

RULES TO DETERMINE IF A DIGIT IS SIGNIFICANT:  All non-zero digits are significant  Any zeroes placed after other digits and behind a decimal are significant  Any zeroes placed between significant digits are significant  All other zeroes are not significant e.g. both 100 cm and kg each have only one significant digit

HOW MANY SIGNIFICANT DIGITS ARE THERE IN EACH OF THE FOLLOWING?  1.10 A  h  MHz  2100 kJ    kg  km

THE FINAL ANSWER  When a measurement is used in a calculation, the final answer must take into consideration the uncertainty in the original measurements.  Note: Exact numbers used in calculations (e.g. a factor such as ½ in the equation K=½mv 2 ) are not measurements and do not have any uncertainty.

ADDITION AND SUBTRACTION  When adding or subtracting measurements, the final answer should be rounded off to the least number of decimals in the original measurements. e.g cm (3 decimal places) cm (2 decimal places) 5.13 cm (2 decimal places)

MULTIPLICATION AND DIVISION  When multiplying or dividing measurements, the final answer should be rounded off to the same number of sig digs as are in the measurement with the least number of sig digs. e.g cm (4 sig digs) x0.01 cm (1 sig dig) 0.05 cm 2 (1 sig dig)