Standard Units are universally accepted units of measurement that serve as a common reference point for quantifying physical quantities. They ensure that measurements taken by different scientists or in different locations are comparable and consistent, facilitating accurate communication of results across the global scientific community. By using standard units, scientists can compare experimental data, verify findings, and reproduce experiments without confusion or the need for complex conversions.
Le Système International d’unités (SI) is the international system of measurement adopted for scientific purposes. It provides a comprehensive set of units, symbols, and prefixes for all known quantities. The SI system includes seven base quantities, each with a designated base unit, such as the metre for length or the kilogram for mass. The SI system ensures uniformity in measurements worldwide, eliminating discrepancies that could arise from using different measurement systems.
The use of standard units is crucial because it guarantees that scientists across the globe can compare and reproduce results without confusion. When measurements are expressed in a common system, such as SI, it becomes straightforward to verify experimental outcomes, share data, and build upon each other's work. This consistency is fundamental to the progress of scientific knowledge, as it prevents misunderstandings that could occur from using different units or measurement systems.
Furthermore, employing a common system of units helps avoid errors that might result from unit conversion between countries or regions. For example, if one scientist reports a length in inches and another in centimeters, there is a risk of miscalculating or misinterpreting the data during conversion. Using SI units, which are standardized and universally recognized, minimizes such risks and enhances the accuracy of measurements.
Finally, standard units serve as a reference for all physical measurements in experiments. Whether measuring mass, length, time, electric current, temperature, amount of substance, or luminous intensity, each quantity has a designated base unit within the SI system. These units provide a consistent framework, allowing scientists to communicate measurements clearly and unambiguously, and to derive other units (called derived units) based on the base units.
Understanding why universal measurement standards are essential highlights their role in ensuring clear, consistent scientific communication. Standard units enable scientists worldwide to compare, verify, and reproduce results accurately, fostering collaboration and advancing scientific knowledge without confusion or error.
There are seven fundamental base quantities in the SI system used to define all other units. These base quantities serve as the foundational measurements from which other derived units are constructed, ensuring consistency and universality in scientific measurement. Each base quantity is associated with a specific, unique unit and symbol, which provides a standardized way to express and communicate measurements across different contexts and disciplines.
Base Quantities: The seven fundamental physical quantities in SI that form the basis for all measurement units. These quantities are essential for describing the physical universe and are used to derive all other units in the system.
Kilogram (kg): The SI unit of mass. It is the base unit used to quantify the amount of matter in an object. The kilogram is symbolized as "kg" and is fundamental in measurements involving weight, mass, and inertia.
Metre (m): The SI unit of length. It is used to measure the distance or size of objects and is symbolized as "m". The metre provides a standard measure for spatial dimensions in physics and engineering.
Second (s): The SI unit of time. It is used to quantify durations and intervals and is symbolized as "s". Accurate measurement of time is crucial for dynamics, oscillations, and many other physical phenomena.
Ampere (A): The SI unit of electric current. It measures the flow of electric charge and is symbolized as "A". The ampere is fundamental in electrical and electronic measurements.
Kelvin (K): The SI unit of thermodynamic temperature. It is used to measure absolute temperature and is symbolized as "K". The Kelvin scale starts at absolute zero, the point where particles have minimum thermal motion.
Luminous Intensity: Although it is a base quantity in the SI system, luminous intensity is not required for exams. It measures the perceived power of light emitted by a source in a particular direction, with the unit candela (cd).
There are seven fundamental base quantities in SI used to define all other units. Each base quantity has a unique unit and symbol, such as kilogram (kg) for mass, metre (m) for length, second (s) for time, ampere (A) for electric current, and kelvin (K) for temperature. Luminous intensity is also a base quantity but is not required for exams. Memorizing these seven units and their symbols is essential because they form the foundation for all measurements in physics, enabling precise communication and calculation of physical quantities.
Memorizing and recalling the seven fundamental base units in SI is essential because they form the foundation for all physics measurements. Understanding these units and their symbols ensures accurate measurement, calculation, and communication of physical quantities across various scientific disciplines.
Derived Units are units of measurement that are formed by combining the base units according to algebraic relationships. They are not fundamental units themselves but are constructed from the fundamental units to express quantities such as area, volume, speed, and force. For example, the unit of force, the newton (N), is a derived unit expressed as kg·m/s², combining the base units of mass, length, and time.
Algebraic Unit Manipulation involves applying algebraic rules—such as addition, subtraction, multiplication, and division—to units when working with equations. This process allows for the derivation of complex units from simpler, base units by algebraically manipulating the equations that define physical quantities. For instance, when deriving the unit of pressure, the force (in newtons) divided by area (in square meters) involves dividing the units N by m², resulting in the unit of pressure: pascal (Pa).
Unit Substitution is the method of replacing a quantity in an equation with its equivalent expressed in base units. This process is essential for deriving the units of a new quantity or for converting between different units. For example, to find the unit of work, which is force times distance, one substitutes force with kg·m/s² and distance with meters (m), leading to the unit of work as kg·m²/s², known as the joule (J).
Volume Unit Derivation involves starting from the basic units of length and algebraically combining them to express volume. Since volume is a measure of three-dimensional space, its unit is derived by cubing the length unit. For example, the cubic meter (m³) is derived from the base unit of length (meter) by raising it to the third power, representing the volume of a cube with sides of one meter.
Derived units are formed by combining base units through algebraic expressions that mirror the physical relationships between quantities. These combinations are expressed algebraically, following the rules of algebra: units in multiplication are combined by multiplying their units, and units in division are combined by dividing their units. For example, speed is derived from distance over time, resulting in units of m/s, which is obtained by dividing the unit of length (meters) by the unit of time (seconds).
When deriving a derived unit, the process begins with the defining equation of the physical quantity. To find the unit, substitute each variable with its corresponding base units. This substitution allows you to algebraically manipulate the units to arrive at the unit of the derived quantity. For example, to derive the unit of acceleration, start from the equation . Replace with m/s and with s, then divide, resulting in m/s² as the unit of acceleration.
In practice, understanding how to manipulate units algebraically is crucial for ensuring consistency in calculations and for deriving new units from known quantities. This skill enables you to interpret complex units correctly and to verify the dimensional consistency of equations.
Mastering the algebraic manipulation of units and equations allows you to derive complex units from fundamental base units, ensuring accurate and consistent measurement of physical quantities. This skill is essential for understanding the relationships between different quantities and for solving problems involving derived units.
Homogeneity refers to the property of an equation where the units on both sides match exactly. This means that the units of measurement in the terms on one side of the equation are identical to those on the other side, ensuring that the equation is dimensionally consistent. For example, if one side of an equation is expressed in Newtons, the other side must also be in Newtons for the equation to be considered homogeneous.
Unit Consistency in Equations is the principle that, when formulating or analyzing an equation, the units of all terms must be compatible and correctly aligned. This ensures that the equation makes physical sense and adheres to the rules of dimensional analysis. Checking for unit consistency involves verifying that each term in the equation has the same units or that the units combine appropriately according to the mathematical operations involved.
Dimensional Analysis is a method used to verify the correctness of an equation by examining the units involved. It involves analyzing the units of each term to confirm that they are consistent across the equation. This process helps identify errors in the formulation of equations and ensures that the equations are dimensionally valid before applying them to physical problems.
An equation is homogeneous if the units on both sides match exactly. This means that the units are identical in type and magnitude, not just compatible or similar. For example, an equation equating force (in Newtons) to mass (in kilograms) multiplied by acceleration (in meters per second squared) is homogeneous because Newtons are defined as kg·m/s², ensuring units on both sides are consistent.
Testing homogeneity is a crucial step in verifying whether an equation is dimensionally correct. By checking that the units on each side of the equation are the same, one can confirm that the equation is physically plausible and free from fundamental dimensional errors.
It is important to note that homogeneity does not guarantee that the equation is physically correct in all contexts. An equation can be dimensionally consistent yet still be physically incorrect or incomplete. Homogeneity only ensures that the units are compatible, not that the equation accurately describes the physical phenomena.
Using unit analysis to check the dimensional validity of physics equations is an essential preliminary step before applying them in calculations. Ensuring an equation is homogeneous helps confirm that it is dimensionally consistent, which is a necessary condition for physical correctness, although it does not guarantee the equation's overall validity.
Density is a measure of how much mass is contained within a given volume of a substance. It is defined as the ratio of mass to volume, expressed mathematically as density = mass / volume. The SI unit for density is kilograms per cubic metre (kg/m³), which indicates how many kilograms of a substance occupy one cubic metre of space.
Volume refers to the amount of three-dimensional space occupied by an object or substance. It quantifies the capacity of an object in terms of how much space it takes up. The volume of a regularly shaped object, such as a rectangular prism, can be calculated by multiplying its length, width, and height.
Cubic Metre (m³) is the SI unit of volume derived from the cube of the length unit metre. It represents the volume of a cube with edges measuring one metre each. This unit is used to express the volume of large objects or quantities of substances.
Mass per Unit Volume is a way of expressing how dense a substance is, indicating how much mass is contained in each unit of volume. It is the fundamental concept behind the definition of density, linking the amount of matter to the space it occupies.
Density is mass divided by volume with units kg/m³.
This means that to find the density of an object, you divide its total mass (in kilograms) by its total volume (in cubic metres). The resulting value tells you how compact the substance is: higher density indicates more mass packed into a given volume, while lower density indicates less.
Volume is calculated as length × width × height with units m³.
For objects with regular shapes, such as rectangular blocks, the volume can be straightforwardly determined by multiplying the three linear dimensions. This calculation yields the volume in cubic metres, aligning with SI units.
Volume units are derived from the cube of the length unit (metre).
Since volume measures three-dimensional space, its SI unit, the cubic metre, is obtained by cubing the metre (m). This means that if the length is measured in metres, the volume unit is m³, which is conceptually a cube of one metre on each side.
Understanding the relationship between physical quantities like density and volume, along with their SI units, is essential for solving problems involving material properties and measurements. Recognizing that volume units are derived from the cube of length units helps in converting and calculating these quantities accurately in various contexts.
Scalar Quantity: A scalar quantity is a physical quantity that has only magnitude and no direction. It is fully described by a numerical value and the unit associated with that measurement. For example, distance, speed, and mass are scalar quantities because they do not specify any particular direction in space.
Vector Quantity: A vector quantity is a physical quantity that possesses both magnitude and direction. It is represented by a numerical value, a unit, and a specific direction in space. Examples include displacement, velocity, and force. Vectors are often depicted graphically as arrows, where the length of the arrow indicates magnitude and the arrowhead indicates direction.
Resultant Vector: The resultant vector is the single vector that results from the vector addition of two or more vectors acting on the same point or object. It represents the overall effect of multiple vectors combined. For example, when two forces act on an object, the resultant force is the vector sum of those forces, indicating the net effect on the object.
Vector Components: Vector components are the projections of a vector along specified axes, typically the horizontal and vertical axes. They are the parts of a vector resolved into perpendicular directions, which can be used to analyze the vector’s effect along each axis separately. For example, a velocity vector can be resolved into horizontal and vertical components using trigonometric functions.
Co-planar Vectors: Co-planar vectors are vectors that lie within the same plane. They can be added or resolved within that plane using vector addition or resolution techniques. For example, two forces acting on an object in the same flat surface are co-planar vectors.
Scalars have magnitude only; vectors have both magnitude and direction. This fundamental difference means that scalar quantities can be described by a single numerical value with units, while vectors require both magnitude and a specified direction to be fully described.
When vectors are along the same line of action, they can be added algebraically. This means that if two vectors act along the same straight line, their magnitudes can be summed or subtracted directly, depending on their directions, to find the resultant vector.
The resultant vector can be found using Pythagoras’ theorem when the vector components are perpendicular. If the horizontal and vertical components of a vector are known, the magnitude of the resultant vector is calculated as the square root of the sum of the squares of these components.
Vector components can be resolved using trigonometric functions. Specifically, the horizontal component of a vector can be found using cosine of the angle it makes with the horizontal, while the vertical component can be found using sine of that angle. These components allow for easier analysis and addition of vectors in different directions.
Understanding the difference between scalar and vector quantities is essential for analyzing physical phenomena. Mastering vector addition, including the use of components and Pythagoras’ theorem, enables accurate calculation of the combined effects of multiple vectors in a plane.
Newton (N): A Newton is the SI unit of force. It is defined as the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared. This definition stems directly from the fundamental SI base units, which are kilogram (kg) for mass, meter (m) for length, and second (s) for time. Therefore, 1 Newton (N) = 1 kg·m/s². This means that when a force of 1 Newton is applied to an object with a mass of 1 kg, it causes the object to accelerate at 1 m/s².
Joule (J): The Joule is the SI unit of energy. It is derived from the force unit Newton and the distance unit meter. Specifically, 1 Joule is the work done or energy transferred when a force of 1 Newton acts over a distance of 1 meter in the direction of the force. Mathematically, this is expressed as 1 Joule = 1 N·m. This derivation links energy directly to force and distance, emphasizing the physical meaning of energy as the capacity to do work through a force acting over a displacement.
Understanding how units are derived from base SI units helps in verifying and analyzing equations involving force and energy. For force, the unit Newton (N) is explicitly defined as 1 kg·m/s², which connects the concept of force to the fundamental units of mass, length, and time. This derivation confirms that force is fundamentally related to how mass responds to acceleration, as described by Newton's second law.
Similarly, the energy unit Joule (J) is derived as the product of force and distance, specifically 1 N·m. Recognizing this derivation is crucial because it allows us to verify energy calculations and understand the physical meaning behind energy units. When an energy value is expressed in Joules, it signifies the work done by a force over a certain distance, linking the abstract unit to a tangible physical process.
Connecting force and energy units back to their base SI units provides a clearer understanding of their physical meaning. It emphasizes that force relates to how mass accelerates, while energy relates to the capacity to perform work through forces acting over distances. This foundational understanding is essential for analyzing and verifying equations involving force and energy in physics problems.
Connecting force and energy units back to base SI units reveals their physical significance: force measures how mass responds to acceleration, and energy quantifies the work done by force over a distance. This understanding helps in verifying equations and grasping the real-world meaning of these units in physical phenomena.
Force
Force is an interaction that causes a change in an object's motion or shape. It is a vector quantity, meaning it has both magnitude and direction. According to the source content, force is the agent that causes acceleration, as described by Newton’s second law. It can be exerted through contact or at a distance, and its effect is to alter the velocity or deformation of an object.
Acceleration
Acceleration is the rate at which an object’s velocity changes over time. It is directly caused by the application of force, as per Newton’s second law. Acceleration can be positive (speeding up), negative (slowing down), or change direction, and its magnitude is measured in units of meters per second squared (m/s²).
Velocity
Velocity is the speed of an object in a specified direction. It is a vector quantity, meaning it includes both magnitude and direction. Velocity describes how fast an object moves and in which direction, and it can change due to acceleration.
Displacement
Displacement is the shortest straight-line distance from an object’s initial position to its final position, considering direction. It is a vector quantity, and it differs from distance in that it accounts for the overall change in position, not the total path traveled.
Equation of Motion
The equation of motion relates velocity, acceleration, and displacement of an object under uniform acceleration. It provides a mathematical framework to predict an object’s future position and velocity based on initial conditions and constant acceleration. The specific form of the equation is not explicitly given in the source content, but it is understood to connect these quantities systematically.
Force causes acceleration according to Newton’s second law. This law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. When a force acts on an object, it results in a change in the object’s velocity over time, which is the acceleration.
Equations of motion relate velocity, acceleration, and displacement. These equations serve as fundamental tools for analyzing the motion of objects under constant acceleration, allowing calculation of unknown quantities such as final velocity or displacement when initial conditions and acceleration are known.
Units of each quantity must be consistent when applying motion laws. For example, when calculating acceleration, velocity should be in meters per second (m/s), displacement in meters (m), and time in seconds (s). Consistent units are essential to ensure accurate and meaningful results in physics calculations involving motion.
Applying the fundamental laws of motion requires careful attention to the relationships between force, acceleration, velocity, and displacement, as well as ensuring the consistency of units. Doing so guarantees accurate and reliable physics calculations.
Newton’s First Law: This law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In other words, if no net force acts on an object, its velocity will not change, and it will continue doing what it was already doing—either staying still or moving at a constant speed in a straight path.
Newton’s Second Law: This law provides a quantitative relationship between force, mass, and acceleration. It states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, expressed mathematically as F = ma. This means that the acceleration of an object depends directly on the applied force and inversely on its mass.
Newton’s Third Law: This law states that for every action, there is an equal and opposite reaction. When one object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction on the first object. This principle explains interactions such as the recoil of a gun or the propulsion of a rocket.
Inertia: Inertia is the property of an object that resists changes to its state of motion. It is directly related to mass; the greater the mass, the greater the inertia, and the harder it is to start moving an object or to stop it once it is moving.
Action-Reaction: This term describes the pair of forces described by Newton’s Third Law. When an action force is exerted by one object on another, the reaction force is exerted by the second object back on the first, with both forces being equal in magnitude and opposite in direction.
The First Law emphasizes that an object will not change its state of motion unless an external force acts upon it. This means that if an object is at rest, it will stay at rest; if it is moving at a constant velocity, it will continue to do so unless influenced by an external force. The law highlights the concept of inertia, which is the tendency of objects to resist changes in their motion.
The Second Law introduces a way to measure and predict the effects of forces on objects. It states that force is directly proportional to the product of an object’s mass and its acceleration, summarized by the equation F = ma. This law allows us to quantify how different forces influence the motion of objects, making it fundamental for understanding dynamics.
The Third Law explains the reciprocal nature of forces in interactions. When one object exerts an action force on another, the second object responds with an equal and opposite reaction force. This principle is crucial for understanding phenomena such as walking (where the ground pushes back against your foot) and rocket propulsion (where expelled gases push the rocket forward).
Inertia is the resistance to change in motion, directly linked to an object’s mass. The more massive an object, the more inertia it has, and the more force is needed to alter its velocity.
The Action-Reaction concept is the manifestation of Newton’s Third Law, illustrating that forces always come in pairs during interactions, with each force acting on a different object but being equal and opposite.
Understanding Newton’s three laws of motion is fundamental to grasping how forces influence the movement of objects. These laws describe the conditions under which objects stay at rest or in motion, how forces cause acceleration, and how interactions between objects always involve equal and opposite forces, all rooted in the core concept of inertia.
Free-Body Diagram
A free-body diagram is a visual representation that shows all the forces acting on an object. It simplifies the analysis by isolating the object and illustrating each force with an arrow, where the arrow's length indicates the magnitude of the force and its direction shows the force's direction. This diagram helps in understanding how forces interact and balance on the object.
Equilibrium
An object is said to be in equilibrium when the resultant force acting upon it is zero. This means that all the forces acting on the object cancel each other out, resulting in no change in the object's motion. In equilibrium, the object may be at rest or moving with constant velocity, but it does not accelerate.
Resultant Force
The resultant force is the single force that has the same effect as all the individual forces acting on an object combined. It is found by vector addition of all forces. When the resultant force is zero, the forces are balanced, and the object remains in equilibrium.
Balanced Forces
Balanced forces are forces that are equal in magnitude and opposite in direction, resulting in no net force acting on the object. When forces are balanced, no acceleration occurs, and the object either remains at rest or continues to move at a constant velocity.
Force diagrams visually represent all forces acting on an object, providing a clear and simplified view of the force interactions. These diagrams are crucial tools in analyzing whether an object is in equilibrium or not. When examining an object, if the force diagram shows that the resultant force is zero, then the object is in equilibrium. This condition indicates that the forces are balanced, meaning that their effects cancel each other out. As a result, no acceleration occurs, and the object maintains its state of motion—either remaining at rest or moving uniformly in a straight line. Recognizing these key points allows us to analyze physical situations effectively, using force diagrams to determine whether forces are balanced and whether the object is in equilibrium.
Using force diagrams to analyze the forces acting on an object enables us to determine if the object is in equilibrium. When the resultant force is zero, the forces are balanced, and no acceleration occurs, helping us understand the force balance in various situations.
Moment is the measure of the turning effect of a force applied to an object about a specific point or axis. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the pivot point to the line of action of the force. This perpendicular distance is known as the lever arm. The formula for the moment (also called torque in some contexts) is expressed as:
Torque is the same as the moment and refers to the rotational effect produced by a force. It causes an object to rotate or helps maintain rotational equilibrium. The magnitude of torque depends on the size of the force and the distance from the pivot point at which the force is applied, emphasizing the importance of the perpendicular component of the force relative to the lever arm.
Lever Arm is the shortest perpendicular distance from the pivot point to the line of action of the applied force. It determines the effectiveness of a force in producing rotational motion: the longer the lever arm, the greater the moment or torque produced by a given force.
Rotational Equilibrium occurs when the sum of all moments acting on a body about any pivot point is zero. In this state, there is no net rotational motion, meaning the clockwise moments balance the counterclockwise moments. Achieving rotational equilibrium involves correctly identifying all forces and their respective lever arms to ensure their moments sum to zero.
The moment of a force is obtained by multiplying the force by the perpendicular distance from the pivot to the line of action of that force. This emphasizes the importance of the force's direction and the correct identification of the lever arm for accurate calculation.
Torque is the cause of rotational motion or the condition of rotational equilibrium. When a torque is unbalanced, it results in angular acceleration, causing the object to rotate. When balanced, the torques cancel out, and the object remains in rotational equilibrium.
Calculating moments requires careful identification of force direction and the lever arm. The force must be considered in its perpendicular component relative to the lever arm; if the force is not perpendicular, only the perpendicular component contributes to the moment.
Understanding how forces produce rotation through moments and applying the concept of torque enables us to analyze and predict the conditions for rotational equilibrium, ensuring that forces are balanced and objects remain stable or rotate as intended.
Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. The mathematical expression for momentum (p) is:
where is the mass of the object and is its velocity. Because it is a vector, the momentum of an object depends on the direction of its velocity, and when analyzing interactions, the vector nature must be considered.
Impulse is the effect of a force acting over a period of time, which results in a change in an object's momentum. It is equal to the product of the force applied and the time duration over which it acts:
Impulse has the same units as momentum (e.g., kg·m/s) and directly relates to the change in momentum of an object, as expressed by the impulse-momentum theorem.
Closed System refers to a collection of objects or particles where no external forces act upon the system as a whole. In such a system, the total momentum remains constant before and after any interaction or event, assuming no external influences.
Conservation Principle states that within a closed system, the total momentum before an interaction is equal to the total momentum after the interaction. This principle is fundamental in analyzing collisions and interactions, allowing the prediction of outcomes based on initial conditions.
Momentum is mass times velocity, a vector quantity.
This means that when calculating or analyzing momentum, both the magnitude and the direction of velocity are crucial. For example, two objects moving at the same speed but in opposite directions will have momenta of equal magnitude but opposite signs, resulting in a net momentum that depends on their directions.
In a closed system, total momentum before and after an event is conserved.
This implies that if no external forces are acting on the system, the sum of the momenta of all objects involved remains unchanged through the interaction. Whether objects collide elastically or inelastically, the total momentum remains constant, enabling the analysis of such events without external interference.
Impulse changes momentum and equals force times time.
When a force acts on an object over a certain time interval, it imparts an impulse, which results in a change in the object's momentum. The greater the force or the longer it acts, the larger the change in momentum. This relationship is crucial for understanding how forces influence motion during interactions.
The principle of conservation of momentum allows us to analyze and predict the outcomes of collisions and interactions within a closed system by equating the total momentum before and after the event. Impulse serves as the link between force application and changes in momentum, emphasizing how forces over time influence motion.
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| Concept | Description | Key Authors / References |
|---|---|---|
| Standard Units | Universally accepted units ensuring measurement consistency and comparability across scientific communities. | None specified |
| SI System | International system of measurement with 7 base quantities, providing uniformity worldwide. | None specified |
| Base SI Units | Fundamental units for physical quantities: kilogram (kg), metre (m), second (s), ampere (A), kelvin (K), candela (cd). | None specified |
| Derived Units | Units formed by combining base units algebraically, e.g., newton (N) = kg·m/s², pascal (Pa) = N/m², joule (J) = kg·m²/s². | None specified |
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Importance of standard units
Ensure consistent, comparable measurements worldwide.
SI — full form?
International System of Units
Base SI units — number?
Seven fundamental units define all SI measurements.
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