Summary

• Physics is about trying to find the simple laws that describe all natural phenomena.
• Physics operates on a vast range of scales of length, mass, and time. Scientists use the concept of the order of magnitude of a number to track which phenomena occur on which scales. They also use orders of magnitude to compare the various scales.
• Scientists attempt to describe the world by formulating models, theories, and laws.

• Systems of units are built up from a small number of base units, which are defined by accurate and precise measurements of conventionally chosen base quantities. Other units are then derived as algebraic combinations of the base units.
• Two commonly used systems of units are English units and SI units. All scientists and most of the other people in the world use SI, whereas nonscientists in the United States still tend to use English units.
• The SI base units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively.
• SI units are a metric system of units, meaning values can be calculated by factors of 10. Metric prefixes may be used with metric units to scale the base units to sizes appropriate for almost any application.

• To convert a quantity from one unit to another, multiply by conversion factors in such a way that you cancel the units you want to get rid of and introduce the units you want to end up with.
• Be careful with areas and volumes. Units obey the rules of algebra so, for example, if a unit is squared we need two factors to cancel it.

• The dimension of a physical quantity is just an expression of the base quantities from which it is derived.
• All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.

• An estimate is a rough educated guess at the value of a physical quantity based on prior experience and sound physical reasoning. Some strategies that may help when making an estimate are as follows:
  • Get big lengths from smaller lengths.
  • Get areas and volumes from lengths.
  • Get masses from volumes and densities.
  • If all else fails, bound it.
  • One “sig. fig.” is fine.
  • Ask yourself: Does this make any sense?

• Accuracy of a measured value refers to how close a measurement is to an accepted reference value. The discrepancy in a measurement is the amount by which the measurement result differs from this value.
• Precision of measured values refers to how close the agreement is between repeated measurements. The uncertainty of a measurement is a quantification of this.
• The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool.
• Significant figures express the precision of a measuring tool.
• When multiplying or dividing measured values, the final answer can contain only as many significant figures as the value with the least number of significant figures.
• When adding or subtracting measured values, the final answer cannot contain more decimal places than the least-precise value.

The three stages of the process for solving physics problems used in this book are as follows:

• Strategy: Determine which physical principles are involved and develop a strategy for using them to solve the problem.
• Solution: Do the math necessary to obtain a numerical solution complete with units.
• Significance: Check the solution to make sure it makes sense (correct units, reasonable magnitude and sign) and assess its significance.