Kinematics Fundamentals and Essential Lab Equipment
Core Concepts in Kinematics
Kinematics
Kinematics is the branch of physics that studies the velocity and acceleration of a moving object, without considering the forces that cause the motion.
Observer Reference System
The Observer Reference System is used for measuring the position, velocity, and acceleration of a moving object. These are typically Cartesian coordinates (e.g., $xy$-plane or $xyz$-space).
Trajectory (Path)
The Trajectory is the line that results from the union of all points through which the object passes.
Position Vector
The Position Vector is used to determine the position of an object in a particular movement (represented by an arrow).
Physical Quantities and Vectors
Physical Quantity (Magnitude)
A Physical Quantity is any property that can be measured:
- Scalar Quantities: Those that are defined solely by a numerical value (magnitude), such as temperature, mass, or shoe size.
- Vector Quantities: Those that, in addition to the numerical value, require a direction and a sense (orientation). They are represented by a vector (e.g., speed, acceleration, force).
Vector
A Vector is a mathematical element represented by an arrow that has three components:
- Magnitude (Length): Always represents the numerical value.
- Direction: The line that supports the vector.
- Sense (Orientation): Is indicated by the arrowhead (the peak).
Note: A vector is represented by a letter with an arrow on top and always has an origin.
Velocity and Acceleration
Velocity
Velocity is a vector quantity whose magnitude (speed) is defined as the distance traveled by the object per unit of time. It is measured in meters per second ($ ext{m/s}$) in the International System (SI) or kilometers per hour ($ ext{km/h}$).
Acceleration
Acceleration exists in a movement when there is a variation of the velocity. It is considered positive ($+$) if the velocity is increasing and negative ($-$) if it is decreasing.
Types of Motion
Uniform Rectilinear Motion (MRU)
In Uniform Rectilinear Motion (MRU), the trajectory of the object is a straight line, and the velocity vector (magnitude, direction, and sense) is constant. (This implies zero acceleration.)
Uniformly Varied Rectilinear Motion (MRUV)
In Uniformly Varied Rectilinear Motion (MRUV), the path is a straight line, and the magnitude of the speed varies uniformly (constant acceleration).
Uniform Circular Motion (MCU)
In Uniform Circular Motion (MCU), the object describes a circular trajectory with constant speed.
Related Concepts in MCU
- Radian (rd): The unit for measuring angles. A radian is the angle whose arc length is equal to its radius.
- Period (T): The time required for the object to complete one full turn, measured in seconds ($ ext{s}$).
- Frequency (f): The number of turns the object completes in one second, designated as $f$ and expressed in Hertz ($ ext{Hz}$).
Essential Laboratory Techniques
Pipetting
Pipetting is used to take small amounts of liquid and then slowly release them. Note: This procedure requires the use of mechanical aids (e.g., pipette bulbs) and should never be performed using the mouth.
Gauging (Enrase)
Gauging (Enrase) is the process where the liquid meniscus is aligned tangentially to the capacity line (calibration mark) of the glassware.
Using an Electronic Scale
An Electronic Scale typically offers options to weigh to the nearest tenth or hundredth of a unit. To achieve higher precision (e.g., hundredths), the *Cal Mode* button may need to be pressed. The standard procedure is to place the weighing vessel (e.g., a watch glass), remove its weight by pressing the *Tare* button, and then weigh the substance.
Common Laboratory Glassware
Measuring Cylinder
A Measuring Cylinder (or Graduated Cylinder) is used to measure a liquid which will later be used in another container.
Volumetric Flask
A Volumetric Flask is a container with a known calibration mark on the neck that accurately defines the gauging volume of the flask. It is used to prepare solutions with a particular concentration.
Erlenmeyer Flask
The Erlenmeyer Flask is used for reactions and is graduated, but these markings are approximate and not intended for precise volume determination.
Flat-Bottomed Flask
The Flat-Bottomed Flask is used for reactions. It is not graduated but shows the approximate liquid level.
Beaker with Agitator
A Beaker is used for reactions and serves to dissolve some substances. It is graduated, but the markings are approximate.
Burette
A Burette is a graduated instrument that helps us dispense a known volume of reagent in a chemical reaction (titration). The reagent flow is controlled by the stopcock (wheel), normally dispensed drop by drop. It is held by a burette stand (stand, burette clamp, and double nut bar).