AP PHYSICS 1: MOTION NOTES

1.2 - Physical Quantities and Units 

  • Numerical values for physical quantities and equations for physical principles allows us to understand more deeply than qualitative description alone. 

  • Most physical quantities are expressed as combinations of four fundamental physical quantities: length, mass, time and electric current. 

  • Physical quantities: specifying how it is measured by stating how it is calculated from other measurements. 

  • Physical quantities measurements are expressed with units, which are standardized values. 

  • The two main systems of units are SI units (metric system) and English units (imperial system)

SI Units: Fundamental and Derived Units 

  • Fundamental Units: Units that physical quantities are measured in. 

  • Derived Units: can be expressed as algebraic combinations of the four fundamental physical quantities. 

Units of Time, Length, and Mass: The Second, Meter, and Kilogram

  • The Second 

  • SI unit - time: the second (s)

  • Accuracy in the fundamental units are ESSENTIAL, all measurements can be no more accurate than the fundamental units themselves.

    • The Meter 

  • SI unit - length: the meter (m)

  • The length of the meter will change if the speed of light is someday measured with greater accuracy. 

    • The Kilogram

  • SI unit - mass: the kilogram (kg)

  • The kilogram is defined in terms of the second, the meter, and Planck’s constant. 

Metric Prefixes 

  • Metric systems have conversions of units that only involve powers of 10. 

  • The same unit can be used over extremely large ranges of values simply using the appropriate metric prefix. 

  • No need to invent new units. 

  • Order of Magnitude: the scale of a value expressed in the metric system. 

  • Each power of 10 are all different orders of magnitude. 

  • All quantities that can be expressed as a product of a specific power of 10 is the sane order of magnitude. 

Unit Conversion and DImensional Analysis 

  • It is necessary to convert from one type of unit to another. 

  • Write the units that we are given and then multiply them by the conversion factor so the units cancel out. 

1.3 Accuracy, Precision, and Significant Figures 

Accuracy and Precision of a Measurement 

  • Science is based on observation and experimentation, which is measurement. 

  • Accuracy: is how close a measurement is to the correct value for that measurement. 

  • Precision: is how close the agreement is between repeated measurements. 

  • Sometimes you have accurate measurements, but not precise, or vice versa. 

Accuracy, Precision, and Uncertainty

  • Uncertainty: is how much your measured values deviate from a standard or expected value. 

  • Uncertainty is like a disclaimer for your measured values.

  • Uncertainty in a measurement includes: 

    • Limitations of the measuring device 

    • The skill of the person making the measurement 

    • Irregularities in the object being measured 

    • Other factors that affect the outcome is dependent on the situation. 

Percent Uncertainty

  • Expressing uncertainty could be as a percent of the measured value. If A is expressed with uncertainty, A, %unc is: 

  • % unc = AAx 100%

Uncertainties in Calculations 

  • Method of adding percents: The method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation. 

Precision of Measuring Tools and Significant Figures

  • A precise measuring tool is one that can measure values in very small increments. 

  • The more precise the measuring tool, the more precise and accurate the measurement can be. 

  • With measured values, you can only list as many digits as we initially measured with our tool. 

  • Significant Figures: the last digit written down in a measurement is the first digit with some uncertainty. 

Zeros 

  • Leading zeros are not significant because they are only placeholders. 

  • If zeros are in-between they are not placeholders, but significant.

Significant figures in Calculations 

  • When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value. 

  • Multiplication and Division:

    • The result should have the same number of significant figures as the quantity having the least significant figures. 

  • Addition and Subtraction: 

    • The answer can contain no more decimal places than the least precise measurement. 

  • 2.1 - Displacement 

    Position 

    • Position: where it is at any particular (given) time. 

    • You need to identify the position relative to a reference frame.

    Displacement

    • Displacement: If an object moves to which a position change occurs. 

    • Emphasizing the object has been moved, or displaced  

    • x=xf-x0 

    • Delta () - “change in” 

    • Initial position x0 | Final position xf

    • SI Unit for displacement is meter (m). If units aren’t in meters, convert into meters to complete the equations. 

    • Displacement has a direction and magnitude. 

    Distance 

    • Distance is NOT described in displacement, unlike direction. 

    • Distance: is defined as the size or magnitude of the displacement between two positions. 

    • Distance between two positions is NOT the same as distance traveled between them. 

    • Distance traveled is the total length of the path traveled between two positions. 

    • Distance has NO direction. 

    2.3 - Time, Velocity, and Speed

    Time 

    • Measurement of time means measuring a change in physical quantity. 

    • Time = change, (the interval over which change occurs). 

    • SI unit for time is second, s.

    • Elapsed time is the difference between the ending time and beginning time. 

      • t=tf-t0

    • Motion starts at time equal to zero (t0=0)

    • The symbol t is used for elapsed time/change in time.

    Velocity 

    • If you have a large displacement in a small amount of time you have a large velocity. 

    • Velocity has units of distance divided by time. 

    • Average velocity is displacement (change in position) divided by the time of travel.

    • v = xt=xf-x0tf-t0

    • If the starting time is at 0, average velocity equation is much simpler, 

    • v=xt

    • Velocity is a vector because displacement is a vector. 

      • Both magnitude and direction.

    • SI unit for velocity is meters per second (m/s).

    • The average velocity doesn’t tell us about what happens between the starting point and ending point. 

    • We can’t tell from average velocity if there were pauses or back ups.

    • The smaller the time intervals in motion = more detailed the information.

    • The average velocity then becomes the instantaneous velocity/velocity at a specific instant. 

      • The average velocity at a specific instant in time or over a small time interval.

    Speed

    • Speed has NO direction. It is scalar. 

    • Instantaneous speed: is magnitude of instantaneous velocity. 

    • Average speed: is the distance traveled divided by elapsed time. 

    • Distance traveled can be greater than the magnitude of displacement. 

    • Average speed can be greater than average velocity, displacement divided by time. 

    • Average speed is not simply the magnitude of average velocity. 

    • A plot of position or of velocity as a function of time is very useful. 

  • 2.4 - Acceleration  

    • Accelerate = to speed up

    • The greater the acceleration, the greater the change in velocity over a given time. 

    • Average Acceleration is the rate at which velocity changes

      • a=vt=vf-v0tf-t0

      • a is the average acceleration, v is velocity, and t is time.

    • The SI Units for acceleration are m/s2, meters per second squared 

    • Velocity is a vector and has both magnitude and direction. 

    • Change in velocity means change in magnitude (or speed), but also change in direction. 

    • Deceleration: when an object slows down, its acceleration is opposite to the direction of its motion. 

    • Deceleration ALWAYS reduces speed. 

    • Negative acceleration may or may not be deceleration. 

    Instantaneous Acceleration

    • Instantaneous Acceleration a, or the acceleration at a specific instant in time.

    • Obtained by considering an infinitesimally small interval of time. 

    Sign and Direction 

    • Plus means the quantity is right 

    • Minus means it is to the left 

    • It is wrong to interpret negative acceleration as the slowing of an object. 

      • Sometimes positive acceleration, slowed a negative velocity

      • Acceleration has to be in the opposite direction from the velocity 

    • A negative acceleration will increase a negative velocity. 

    • The plus and minus signs give the directions of the accelerations

    • If acceleration has the same sign as the velocity, the object is speeding up. 

    • If acceleration has the opposite sign as the velocity, the object is slowing down.