Torque and Angular Momentum
Last Updated : 14 Jul, 2021
For a rigid body, motion is generally both rotational and translation. If the body is fixed at one point, the motion is usually rotational. It is known that force is needed to change the translatory state of the body and to provide it with linear acceleration. Torque and angular momentum are rotational equivalents of force and momentum. These entities help us change the rotational state of the body. Torques and angular momentum are very useful and are encountered almost everywhere in daily life. The power of the engine and motors is measured by torque. So, while studying any rigid body, it is essential to understand the concepts of torque and angular momentum. Let's look at these concepts in detail.
Torque
Torque is analogous to the force in the case of rotational motion. Consider an example of a door. The position of the door is fixed, it can only rotate around its axis. Then what causes the door to rotate? Force is required, but the force applied to the hinge of the door does not work. So, it is not the force alone, the position to which it is applied matters too.
In rotational motion, the analogous force is torque. This is also called the moment of force. This causes angular acceleration in the body, which means forcing to change the rotational state of the body. Let a particle P be located far from the origin at a point whose position vector is given by \vec{r}. If the force F is acting on the particle, the moment of force is given by,
\tau = \vec{F} \times \vec{r}
Since the cross-product is involved, it is a vector quantity. The magnitude of the torque is given by,
\tau = F.r.sin(\theta)
Here, “r” is the magnitude of the position vector, and θ is the angle between the position vector and force. In the formula, the part “rsinθ” is the perpendicular distance of the force from the axis of the rigid body.
Dimensions of torque are given by ML2T-2. These are also dimensions of energy but, these quantities should not be confused as similar. They are very different quantities.The unit of torque is N-m.
Angular Momentum of Particle
It has been mentioned that torque is analogous to force. In the same way, angular momentum is analogous to linear momentum. This is also a vector product similar to its counterpart torque. Consider a particle P with the linear momentum “p” and a position vector with respect to the origin O. The angular momentum of the particle is denoted by “L”,
L = r × p
The magnitude of angular momentum will be given by,
L = rpsinθ
Where r and p are the magnitudes of the position vector and linear momentum respectively. The angle θ is the angle between the position vector and the linear momentum. Here also “rsin(θ)” is the perpendicular angle between the momentum and the position vector.
Relationship between Angular Momentum and Torque
The relationship between the angular momentum and torque is similar to the relationship between the force and the momentum. Force is the change in momentum of the particle. Similarly, torque is the change in angular momentum of the particle. Differentiating the formula for the angular momentum,
\frac{dl}{dt} = \frac{d}{dt}(r \times p)
Applying the product rule for differentiation,
\frac{dl}{dt} = \frac{d}{dt}(r \times p) = \frac{dl}{dt} = \frac{dr}{dt}\times p + r\times \frac{dp}{dt}
Now, \frac{dr}{dt} is the velocity of the particle, but since it is in the same direction as the momentum,
r x \frac{dr}{dt} = 0
So, now the equation becomes,
\frac{dl}{dt} = \frac{d}{dt}(r \times p)\\ = \frac{dl}{dt} = r\times \frac{dp}{dt}
\frac{dp}{dt} represents the force F,
\frac{dl}{dt} = r \times F \\ = \frac{dl}{dt} = \tau
Thus, this proves that the rate of change of angular momentum is given by torque.
Sample Problems
Question 1: Find out the torque on the door if a force of 10N is applied on the door 0.5m from the hinge.
Answer:
Torque is given by,
\tau = F \times r
Where r is the perpendicular distance of the force from the rotational axis.
Given: r = 0.5m and F = 10N.
Plugging the values in the equation,
\tau = F \times r = \tau = 10 \times 0.5 \\ = \tau = 5 \text{ N-m}
Question 2: Find out the torque on the door if a force of 20N is applied on the door 0.3m from the hinge.
Answer:
Torque is given by,
\tau = F \times r
Where r is the perpendicular distance of the force from the rotational axis.
Given: r = 0.3m and F = 20N.
Plugging the values in the equation,
\tau = F \times r = \tau = 20 \times 0.3 \\ = \tau = 6 \text{ N-m}
Question 3: A body is revolving around an axis in a circular motion with a radius of 0.1m, the momentum of the body is given by 50 Kgm/s. Find the angular momentum of the body.
Answer:
Angular momentum of a body is given by,
l = r × p
Where r is the perpendicular distance of the force from the rotational axis and p is the linear momentum.
Given: r = 0.3m and p = 50Kgm/s.
Plugging the values in the equation,
l = r xp
⇒l =0.3 × 50
⇒l = 15
Question 4: A body is revolving around an axis in a circular motion with a radius of 0.2m, the momentum of the body is given by 70 Kg/s. Find the angular momentum of the body.
Answer:
Angular momentum of a body is given by,
l = r × p
Where r is the perpendicular distance of the force from the rotational axis and p is the linear momentum.
Given: r = 0.2m and p =70 Kg/s.
Plugging the values in the equation,
l = r × p
⇒l =0.2 × 70
⇒l = 14
Question 5: A body is revolving around an axis in a circular motion with a radius of 0.2m, the momentum of the body is given by 70 Kg/s. A torque is applied on the body for 2 seconds and the momentum becomes 120Kgm/s. Find the torque applied to the body.
Answer:
Angular momentum of a body is given by,
l = r × p
Where r is the perpendicular distance of the force from the rotational axis and p is the linear momentum.
Rate of Change in angular momentum gives us the torque.
Initial angular momentum
li = 0. 2 × 70
li = 14
Final angular momentum
li = 0. 2 × 120
li = 24
Rate of change of angular momentum = \frac{l_f - l_i}{t }
\tau = \frac{l_f - l_i}{t } \\ = \tau = \frac{120 - 70}{2} \\ = \tau = \frac{50}{2} \\ = \tau = 25 \text{ N-m}
Question 6: A body is revolving around an axis in a circular motion with a radius of 0.1m, the momentum of the body is given by 50 Kgm/s. A torque is applied on the body for 4 seconds and the momentum becomes 100Kgm/s. Find the torque applied to the body.
Answer:
Angular momentum of a body is given by,
l = r × p
Where r is the perpendicular distance of the force from the rotational axis and p is the linear momentum.
Rate of Change in angular momentum gives us the torque.
Initial angular momentum
li = 0. 1 × 50
li = 5
Final angular momentum
li = 0. 1 × 100
li = 10
Rate of change of angular momentum = \frac{l_f - l_i}{t }
\tau = \frac{l_f - l_i}{t } \\ = \tau = \frac{10 - 5}{4} \\ = \tau = \frac{5}{4} \\ = \tau = 1.25 \text{ N-m}
Similar Reads
CBSE Class 11 Physics Notes CBSE Class 11 Physics Notes 2023-24 is a comprehensive guide for CBSE Class 11 students. The class 11 syllabus is designed to provide students with a strong foundation in the basic principles of physics, including Measurement, Vectors, Kinematics, Dynamics, Rotational Motion, Laws of Motion, and Gra
12 min read
Chapter 1 - UNITS AND MEASUREMENT
MeasurementMeasurement is the process of finding out how much, how big, or how heavy something is. It’s like a way to compare things using a standard unit. For example:How long? We measure length using units like inches, feet, or meters.If you measure the height of a door, you’re finding out how many meters or
6 min read
System of UnitsMeasurement forms the fundamental principle to various other branches of science, that is, construction and engineering services. Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurements find a role in everyday activities to a
9 min read
Significant FiguresIn order to find the value of different sizes and compare them, measurement is used. Measuring things is not only a concept but also practically used in everyday life, for example, a milkman measures milk before selling it in order to make sure the correct amount is served, A tailor always measures
7 min read
Units and DimensionsUnits and Dimensions is a fundamental and essential topic in Physics. For the measurement of a physical quantity, Unit plays a vital role. Unit provides a complete idea about the measurement of a physical quantity. Dimension is a measure of the size or extent of a particular quantity.In this article
7 min read
Dimensional FormulaDimensional Formulas play an important role in converting units from one system to another and find numerous practical applications in real-life situations. Dimensional Formulas are a fundamental component of the field of units and measurements. In mathematics, Dimension refers to the measurement of
7 min read
Dimensional AnalysisMost of the physical things are measurable in this world. The system developed by humans to measure these things is called the measuring system. Every measurement has two parts, a number (n) and a unit(u). The unit describes the number, what this number is and what it signifies. For example, 46 cm,
6 min read
Chapter 2 - MOTION IN A STRAIGHT LINE
What is Motion?Motion is defined as the change in the position of an object with respect to time i.e. when an object changes its position according to time it is said to be in the state of motion. Everything in the universe is in a state of continuous motion, for example, the moon revolves around the planets, the
12 min read
Instantaneous Velocity FormulaThe speed of a moving item at a given point in time while retaining a specific direction is known as instantaneous velocity. With the passage of time, the velocity of an object changes. On the other hand, velocity is defined as the ratio of change in position to change in time when the difference in
4 min read
Instantaneous Speed FormulaVelocity is defined as the rate of change of its position with respect to its frame of reference. It is a vector quantity as it has magnitude and direction. The SI unit of velocity is meter per second or m/s.Whereas speed measures the distance traveled by an object over the change in time. It has ma
5 min read
AccelerationAcceleration is defined as the rate of change in velocity. This implies that if an object’s velocity is increasing or decreasing, then the object is accelerating. Acceleration has both magnitude and direction, therefore it is a Vector quantity. According to Newton's Second Law of Motion, acceleratio
9 min read
Uniform AccelerationUniformly Accelerated Motion or Uniform Acceleration in Physics is a motion in which the object is accelerated at constant acceleration. We have to keep in mind that uniform accelerated motion does not mean uniform velocity i.e. in uniform accelerated the velocity of the object increases linearly wi
8 min read
Relative Velocity FormulaLet us suppose we are travelling on a bus, and another bus overtakes us. We will not feel the actual speed of the overtaking bus, as felt by a person who looks at it, standing by the side of the road. If both the buses are moving at the same speed in the same direction, a person in one bus observes
10 min read
Chapter 3 - MOTION IN A Plane
Scalar and VectorScalar and Vector Quantities are used to describe the motion of an object. Scalar Quantities are defined as physical quantities that have magnitude or size only. For example, distance, speed, mass, density, etc.However, vector quantities are those physical quantities that have both magnitude and dir
8 min read
Product of VectorsVector operations are used almost everywhere in the field of physics. Many times these operations include addition, subtraction, and multiplication. Addition and subtraction can be performed using the triangle law of vector addition. In the case of products, vector multiplication can be done in two
5 min read
Vector OperationsVectors are fundamental quantities in physics and mathematics, that have both magnitude and direction. So performing mathematical operations on them directly is not possible. So we have special operations that work only with vector quantities and hence the name, vector operations. Thus, It is essent
8 min read
Resolution of VectorsVector Resolution is splitting a vector into its components along different coordinate axes. When a vector is expressed in terms of its components, it becomes easier to analyze its effects in different directions. This process is particularly useful when dealing with vector quantities such as forces
8 min read
Vector AdditionA Vectors is defined as,"A quantity that has both magnitudes, as well as direction."For any point P(x, y, z), the vector \overrightarrow{OP} is represented as: \overrightarrow{OP}(=\overrightarrow{r}) = x\hat{i} + y \hat{j} + z\hat{k} Vector addition is a fundamental operation in vector algebra used
11 min read
Projectile MotionProjectile motion refers to the curved path an object follows when it is thrown or projected into the air and moves under the influence of gravity. In this motion, the object experiences two independent motions: horizontal motion (along the x-axis) and vertical motion (along the y-axis). Projectile
15+ min read
Chapter 4 - LAWS OF MOTION
Newton's Laws of Motion | Formula, Examples and QuestionsNewton's Laws of Motion, formulated by the renowned English physicist Sir Isaac Newton, are fundamental principles that form the core of classical mechanics. These three laws explain how objects move and interact with forces, shaping our view of everything from everyday movement to the dynamics of c
9 min read
Law of InertiaIsaac Newton's first law of motion, also called the Law of Inertia, is one of the most important ideas in physics. But before we talk about the law, let’s first understand inertia. Inertia is just a fancy word for the idea that things don’t like to change their state. If something is sitting still,
8 min read
Newton's First Law of MotionBefore the revolutionary ideas of Galileo and Newton, people commonly believed that objects naturally slowed down over time because it was their inherent nature. This assumption stemmed from everyday observations, where things like friction, air resistance, and gravity seemed to slow moving objects.
15+ min read
Newton's Second Law of Motion: Definition, Formula, Derivation, and ApplicationsNewton's Second Law of Motion is a fundamental principle that explains how the velocity of an object changes when it is subjected to an external force. This law is important in understanding the relationship between an object's mass, the force applied to it, and its acceleration.Here, we will learn
15 min read
Newton's Third Law of MotionWhen you jump, you feel the gravitational force pulling you down towards the Earth. But did you know that at the same time, you are exerting an equal force on the Earth? This phenomenon is explained by Newton's Third Law of Motion. Newton's Third Law of MotionNewton's Third Law of Motion is a founda
13 min read
Conservation of MomentumAssume a fast truck collides with a stopped automobile, causing the automobile to begin moving. What exactly is going on behind the scenes? In this case, as the truck's velocity drops, the automobile's velocity increases, and therefore the momentum lost by the truck is acquired by the automobile. Wh
12 min read
Static EquilibriumStatic Equilibrium refers to the physical state of an object when it is at rest and no external force or torque is applied to it. In Static Equilibrium, the word 'static' refers to the body being at rest and the word 'equilibrium' refers to the state where all opposing forces cancel out each other a
9 min read
Types of ForcesForces are an external cause that makes a body move, stop, and increase its velocity and other. There are various types of forces in physics and they are generally classified into two categories that are, Contact Force and Non Contact Force. In general, we define a push and pull as a force, and forc
14 min read
FrictionFriction in Physics is defined as a type of force that always opposes the motion of the object on which it is applied. Suppose we kick a football and it rolls for some distance and eventually it stops after rolling for some time. This is because of the friction force between the ball and the ground.
8 min read
Rolling FrictionRolling Friction is a frictional force that opposes rolling objects. Rolling friction is applicable where the body moves along its curved surfaces. For example, wheels in vehicles, ball bearings, etc. are examples of rolling friction. In this article, we will learn about rolling friction, its defini
10 min read
Circular MotionCircular Motion is defined as the movement of an object rotating along a circular path. Objects in a circular motion can be performing either uniform or non-uniform circular motion. Motion of a car on a bank road, the motion of a bike, the well of death, etc. are examples of circular motion.In this
15+ min read
Solving Problems in MechanicsMechanics is a fundamental branch of Physics that explores how objects move when forces or displacements are applied, as well as how these objects interact with and impact their surroundings. It can be divided into two main areas: statics, which studies objects at rest, and dynamics, which focuses o
9 min read
Chapter 5 - WORK, ENERGY AND POWER
EnergyEnergy in Physics is defined as the capacity of a body to do work. It is the capacity to complete a work. Energy can be broadly categorized into two categories, Kinetic Energy and Potential Energy. The capacity of an object to do the work is called the Energy. In this article, we will learn about, E
10 min read
Work Energy TheoremThe concept "work" is commonly used in ordinary speech, and we understand that it refers to the act of accomplishing something. For example, you are currently improving your understanding of Physics by reading this article! However, Physics may disagree on this point. The Work-energy Theorem explain
13 min read
Work - Definition, Formula, Types of Work, Sample ProblemsIn daily life, you are doing activities like study, running speaking, hear, climbing, gossips with friends and a lot of other things. Do you know? All these activities require some energy, and you get it from your daily food. In our day-to-day life, everyone eats food, gets energy, and does some act
6 min read
Kinetic EnergyKinetic Energy is the energy associated with an object moving with a velocity. For an object of mass m and velocity, its kinetic energy is half of the product of the mass of the object with the square of its velocity. In our daily life, we observe kinetic energy while walking, cycling, throwing a ba
10 min read
Work Done by a Variable ForceUsually, a dancing person is considered to be more energetic compared to a sitting person. A security guard who has been standing at his place the whole day has been working for hours. In real life, this seems obvious, but these terms and definitions work differently when it comes to physics. In phy
6 min read
Potential EnergyPotential energy in physics is the energy that an object possesses as a result of its position. The term Potential Energy was first introduced by a well-known physicist William Rankine, in the 19th century. Gravitational Potential Energy, the elastic potential energy of an elastic spring, and the el
8 min read
Mechanical Energy FormulaMechanical Energy - When a force operates on an object to displace it, it is said that work is performed. Work entails the use of a force to shift an object. The object will gather energy after the job is completed on it. Mechanical energy is the amount of energy acquired by a working object. The me
7 min read
Potential Energy of a SpringA spring is used in almost every mechanical aspect of our daily lives, from the shock absorbers of a car to a gas lighter in the kitchen. Spring is used because of their property to get deformed and come back to their natural state again. Whenever a spring is stretched or compressed, a force is expe
7 min read
PowerPower in Physics is defined as the time rate of the amount of energy converted or transferred. In the SI system (or International System of Units), Watt (W) is the unit of Power. Watt is equal to one joule per second. In earlier studies, power is sometimes called Activity. Power is a scalar quantity
8 min read
Collision TheoryCollision Theory says that when particles collide (strike) each other, a chemical reaction occurs. However, this is necessary but may not be a sufficient condition for the chemical reaction. The collision of molecules must be sufficient to produce the desired products following the chemical reaction
7 min read
Collisions in Two DimensionsA Collision occurs when a powerful force strikes on two or more bodies in a relatively short period of time. Collision is a one-time occurrence. As a result of the collision, the involved particles' energy and momentum change. The collision may occur as a result of actual physical contact between th
9 min read
Chapter 6 - SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Concepts of Rotational MotionRotational motion refers to the movement of an object around a fixed axis. It is a complex concept that requires an understanding of several related concepts. Some of the important concepts related to rotational motion include angular displacement, angular velocity, angular acceleration, torque, the
10 min read
Motion of a Rigid BodyA rigid body is a solid body that has little to no deformation when a force is applied. When forces are applied to such bodies, they come to translational and rotational motion. These forces change the momentum of the system. Rigid bodies are found almost everywhere in real life, all the objects fou
7 min read
Centre of MassCentre of Mass is the point of anybody where all the mass of the body is concentrated. For the sake of convenience in Newtonian Physics, we take the body as the point object where all its mass is concentrated at the centre of mass of the body. The centre of mass of the body is a point that can be on
15 min read
Motion of Center of MassCenter of Mass is an important property of any rigid body system. Usually, these systems contain more than one particle. It becomes essential to analyze these systems as a whole. To perform calculations of mechanics, these bodies must be considered as a single-point mass. The Center of mass denotes
7 min read
Linear Momentum of a System of ParticlesThe mass (m) and velocity (v) of an item are used to calculate linear momentum. It is more difficult to halt an item with more momentum. p = m v is the formula for linear momentum. Conservation of momentum refers to the fact that the overall quantity of momentum never changes. Let's learn more about
8 min read
Relation between Angular Velocity and Linear VelocityMotion is described as a change in position over a period of time. In terms of physics and mechanics, this is called velocity. It is defined as the change in position over a period. Rotational Motion is concerned with the bodies which are moving around a fixed axis. These bodies in rotation motion o
4 min read
Angular AccelerationAngular acceleration is the change in angular speed per unit of time. It can also be defined as the rate of change of angular acceleration. It is represented by the Greek letter alpha (α). The SI unit for the measurement of, Angular Acceleration is radians per second squared (rad/s2). In this articl
6 min read
Torque and Angular MomentumFor a rigid body, motion is generally both rotational and translation. If the body is fixed at one point, the motion is usually rotational. It is known that force is needed to change the translatory state of the body and to provide it with linear acceleration. Torque and angular momentum are rotatio
7 min read
TorqueTorque is the effect of force when it is applied to an object containing a pivot point or the axis of rotation (the point at which an object rotates), which results in the form of rotational motion of the object. The Force causes objects to accelerate in the linear direction in which the force is ap
10 min read
Angular MomentumAngular Momentum is a kinematic characteristic of a system with one or more point masses. Angular momentum is sometimes called Rotational Momentum or Moment of Momentum, which is the rotational equivalent of linear momentum. It is an important physical quantity as it is conserved for a closed system
10 min read
Equilibrium of BodiesThe laws of motion, which are the foundation of old-style mechanics, are three explanations that portray the connections between the forces following up on a body and its movement. They were first expressed by English physicist and mathematician Isaac Newton. The motion of an item is related to the
7 min read
Moment of InertiaMoment of inertia is the property of a body in rotational motion. Moment of Inertia is the property of the rotational bodies which tends to oppose the change in rotational motion of the body. It is similar to the inertia of any body in translational motion. Mathematically, the Moment of Inertia is g
15+ min read
Kinematics of Rotational MotionIt is not difficult to notice the analogous nature of rotational motion and kinematic motion. The terms of angular velocity and angular acceleration remind us of linear velocity and acceleration. So, similar to the kinematic equation of motion. Equations of rotational motion can also be defined. Suc
6 min read
Dynamics of Rotational MotionRigid bodies can move both in translation and rotation. As a result, in such circumstances, both the linear and angular velocities must be examined. To make these difficulties easier to understand, it is needed to separately define the translational and rotational motions of the body. The dynamics o
10 min read
Angular Momentum in Case of Rotation About a Fixed AxisImagine riding a bicycle. As you pedal, the wheels start spinning, and their speed depends on how fast you pedal. If you suddenly stop pedaling, the wheels keep rotating for a while before gradually slowing down. This phenomenon occurs due to rotational motion, where the spinning wheels possess angu
7 min read
Chapter 7 - GRAVITATION
Gravitational ForceHave you ever wondered why the Earth revolves around the Sun and not the other way around? Or why does the Moon remain in orbit instead of crashing into Earth? If the Earth pulls the Moon and the Moon pulls the Earth, shouldn’t they just come together? What keeps them apart?All these questions can b
11 min read
Kepler's Laws of Planetary MotionKepler's law of planetary motion is the basic law that is used to define the motion of planets around the stars. These laws work in parallel with Newton's Law and Gravitation Law and are helpful in studying the motion of various planetary objects. Kepeler's law provides three basic laws which are, K
10 min read
Acceleration due to GravityAcceleration due to gravity (or acceleration of gravity) or gravity acceleration is the acceleration caused by the gravitational force of attraction of large bodies. As we know that the term acceleration is defined as the rate of change of velocity with respect to a given time. Scientists like Sir I
8 min read
What is the Acceleration due to Gravity on Earth ?Take something in your hand and toss it down. Its speed is zero when you free it from your grip. Its pace rises as it descends. It flies faster the longer it goes. This sounds like acceleration. Acceleration, on the other hand, implies more than just rising speed. Pick up the same object and throw i
11 min read
Gravitational Potential EnergyThe energy possessed by objects due to changes in their position in a gravitational field is called Gravitational Potential Energy. It is the energy of the object due to the gravitational forces. The work done per unit mass to bring the body from infinity to a location inside the gravitational field
13 min read
Escape VelocityEscape velocity as the name suggests, is the velocity required by an object to escape from the gravitational barrier of any celestial object. "What happens when you throw a stone upward in the air?" The stone comes back to the Earth's surface. If we throw the stone with a much higher force still it
7 min read
Artificial SatellitesWhen looked at the night sky many heavenly bodies like stars, moon, satellites, etc are observed in the sky. Satellites are small objects revolving or orbiting around a planet or on object larger than it. The most commonly observed and known satellite is the moon, the moon is the satellite of Earth,
8 min read
Binding Energy of SatellitesHumans learn early in life that all material items have a natural tendency to gravitate towards the earth. Anything thrown up falls to the ground, traveling uphill is much more exhausting than walking downhill, Rains from the clouds above fall to the ground, and there are several additional examples
10 min read
Chapter 8 - Mechanical Properties of Solids
Stress and StrainStress and Strain are the two terms in Physics that describe the forces causing the deformation of objects. Deformation is known as the change of the shape of an object by applications of force. The object experiences it due to external forces; for example, the forces might be like squeezing, squash
12 min read
Hooke's LawHooke's law provides a relation between the stress applied to any material and the strain observed by the material. This law was proposed by English scientist Robert Hooke. Let's learn about Hooke's law, its application, and others, in detail in this article. What is Hooke’s Law?According to Hooke's
10 min read
Stress-Strain CurveStress-Strain Curve is a very crucial concept in the study of material science and engineering. It describes the relationship between stress and the strain applied on an object. We know that stress is the applied force on the material, and strain, is the resulting change (deformation or elongation)
11 min read
Modulus of ElasticityModulus of Elasticity or Elastic Modulus is the measurement of resistance offered by a material against the deformation force acting on it. Modulus of Elasticity is also called Young's Modulus. It is given as the ratio of Stress to Strain. The unit of elastic modulus is megapascal or gigapascal Modu
12 min read
Elastic Behavior of MaterialsSolids are made up of atoms based on their atomic elasticity (or molecules). They are surrounded by other atoms of the same kind, which are maintained in equilibrium by interatomic forces. When an external force is applied, these particles are displaced, causing the solid to deform. When the deformi
10 min read
Chapter 9 - Mechanical Properties of Fluids