14, R=10m. Question 4. Relation between Angular and Linear Velocity and Acceleration. Circular Motion. Our meticulously curated collection of chapter-wise notes covers the entire Class 11 Physics syllabus. Preparing the chapter for the exams. Class XI Physics Notes Class 11 Physics notes according to FBISE syllabus. ”. Name the physical quantity which remains same in an uniform circular motion. com/out/magnet-brains ️📚👉 Get All Subjects Dec 4, 2021 · Page 3 : Pre-Medical : Physics, , ALLEN, , CIRCULAR MOTION, , If a particle moves in a plane such that its distance from a fixed (or moving) point remains constant then, its motion is called as circular motion with respect to that fixed or moving point. Frequency:- The number of rotations made by the particle per second is called the frequency of rotation. It is a scalar quantity and it ca. , That fixed point is called the centre and the corresponding distance is called the radius of circular path. Acceleration of body down the plane. I can determine the magnitude and direction of the forces needed for the overall centripetal force. Activities were earlier supposed “to be demonstrated by teachers” as per the CBSE Physics syllabus. Rotational and Circular Motion - Numerical Problems. The approximate maximum speed of car will be, if friction between tyres and road is 0. 1: (a) A particle is moving in a circle at a constant speed, with position and velocity vectors at times t and t + Δt. Centripetal Acceleration 6. Understanding all the important concepts, diagrams, graphs and equations. The revision notes for CBSE Class 9 Science Chapter 8 Motion can benefit you in many ways such as: Revising the chapter in just 15 minutes before the exam. When the position of a body changes in reference to a stationary object, it is said to be in motion. Circular motion is a motion in which the distance of a particle (radius) moving in a plane from a fixed point (centre) remains constant. 26. • Scalar and Vector Quantities. List of all important formulas. Our teachers have designed these concept notes for the benefit of Class 11 students. rotational motion class 11 one shot, rotational motion neet questions, rotational motion all formulas, rotational motion and circular motion, rotational motion and circular motion difference, rotational motion and system of particles, rotational motion advanced problems the projectile motion. 290-291, Scheme 54 PU4, Vijay Nagar, Indore - 452010, Madhya Pradesh, India To download Lecture Notes, Practice Sheet & Practice Sheet Video Solution, Visit MANZIL Batch in Batch Section of PhysicsWallah App/Website. This CBSE notes contains CBSE Key Notes, CBSE Revision Notes, Short Key Notes, images, diagrams of the complete Chapter 8 titled Motion of Science taught in class 9. The field of physics known as mechanics is concerned with the investigation of the motion of tangible objects. Read More. Not only can you study all the topics with the Physics notes. Get revision notes for Circular Motion - CBSE Class 11-science Physics and prepare well for your exam. 1 day ago · FAQs on Laws of Motion Class 11 Notes CBSE Physics Chapter 5 (Free PDF Download) 1. Our teachers have designed these concept notes for the benefit of Jan 6, 2023 · The Physics Notes For Cbse Class 11th are based on the NCERT Syallabus and have been designed by expert teachers from the latest 2024 edition of the NCERT book. Chapter 5 Theory (complete) Chapter 5 Conceptual Questions (complete) Chapter 5 Assignments (selected) Chapter 5 Numerical Questions (selected) 11th Class Physics Chapter 6 Study every day: A student should study Physics class 11 notes,one hour per day for seven days; Read Physics class 11 notes before class: Reading the notes before going to the class makes further chapters get clearer; Become an active learner: Try to learn and grasp the problems as quickly as possible Jan 19, 2024 · Motion in a Plane Class 11 Notes Physics Chapter 4. NEET: Circular Motion | Physics Class 11 - NEET See full list on khanacademy. Class 11 Menu Toggle. 4 Centripetal force. Vertical circular motion (VCM) is a special type of circular motion in which the body travels in a vertical plane. Our 1st year physics notes divided into three categories, Chapter Notes, Solved Short Questions and Numerical Notes, and Complete Chapter MCQs Notes. , [M°L°T°]. If a particle is traveling in a circle, it must be experiencing some acceleration towards the center, causing it Since the object is accelerating, there must be a force to keep it moving in a circle. Chapter 7: Gravitation. All Revision notes for Class 11 Physics have been designed as per the latest syllabus and updated chapters given in your textbook for Physics in Standard 11. These pdf notes cover the following topics (1) Displacement (2) Velocity (3) Acceleration (4) Projectile motion (5) Uniform Circular motion (6) Relative motion. For example, motion of a train along a straight line, freely falling body under gravity etc. 2 mv. NEET. N = mgcosθ – mv 2 /2. Circular motion is a familiar class of motion that has a special significance in daily-life situations. 📲PW App Link - Answer: (a) Given: Mass of the block = m Friction coefficient between the ruler and the block = μ Let the maximum angular speed be ω1 for which the block does not slip Now, for the uniform circular motion in the horizontal plane, we have: μ m g = m ω 1 2 L ∴ ω 1 = μ g L (b) Let the block slip at an angular speed ω2. → Motion can be of different types depending Jan 19, 2024 · Law of Motion Class 11 Notes Physics Chapter 5. /. This is just the name given to this type of force and this centripetal force can arise from tension, friction, etc. A particle moving along a straight-line or a path is said to undergo one dimensional motion. Class 10 – General. A particle moving in a plane is said to undergo two NCERT Solutions for Class 11 Physics (Chapter-wise) Chapter 1: Units and Measurements. 3. Definition of Vertical Circular Motion. , projectile motion, circular motion etc. Uniform Circular Motion is the motion of a body traveling at a constant speed along a circular path. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Class 11 Physics Notes. com/playlist?list=PLY0QRf2HggE9ajayGpc5rYrmj1f8SkkaWhttps://www. Solution: Given, π=3. Rotational and Circular Motion – Exercise. • Force Force is an external cause in the form of push or pull, which produces or tries to produce motion in a body at rest, or stops/tries May 27, 2024 · One class 11 Physics test is also there for your practice. Q. Watch his video lectures, download his PDF notes and Ans. Three Dimensional MotionIf all the three coordinates specifying the position of the object changes with respect t. com/playlist?list=PLY0QRf2HggE8E0dr77Y3QYLfRkLQSRKWoh Sep 12, 2022 · Figure 4. Motion in a vertical circle. pabbly. v = u + at → ω = ω 0 + αt s = ut + 1 2 at2 → θ = ω 0 t + 1 2 αt2 v 2 = u + 2as → ω2 = ω2 0 + 2αθ A disc has initial angular speed ω 0 = 10p rad/s. 5 Rotational and Circular Motion Assignments ⇛ Class 11 Physics Ch. 5 Rotational and Circular Motion Conceptual Questions Topics and Subtopics in NCERT Solutions for Class 11 Physics Chapter 4 Motion in a plane: QUESTIONS FROM TEXTBOOK. Applications of banking. DistanceThe length of the. Tired of Ads? Newton's laws of motion and kinematic principles are applied to describe and explain the motion of objects moving in circles; specific applications are made to roller coasters and athletics. Total displacement of the body, D=2R = 2 x 10 = 20 m. A 5 kg iron sphere feels an upsurge of velocity from 2 m/s to 4 m/s. Newton's Universal Law of Gravitation is then presented and utilized to explain the circular and In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Circular and Rotational Motion, as well as the following standards: (4) Science concepts. , The vector joining the centre of Circular Motion and Satellite Motion. g. Uniform Circular Motion Definition: If the magnitude of the velocity of the particle in circular motion remains constant, then it is called uniform circular motion. Nov 17, 2023 · Circular Motion. Angular Acceleration. These notes are made in simple language which is understandable to students without having prior knowledge of chapters. Go Premium with just USD 4. No, since acceleration is always towards the centre. • Motion: A body is said to be in a state of motion when its position change continuously with reference to a point. c = = mω r. Angular Velocity. Total distance travelled by the object. Circular Motion:-. N = mgcosθ + mv 2 /2. or combinations. These revision notes are made by master teachers at Vedantu, who know just what you Uniform Circular Motion -Motion In Plane Class 11 PhysicsNEET Physics Class11Circular MotionAngular velocityangular accelerationClass 11 Physics Uniform Circ Rotational Motion Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes. 1. May 24, 2021 · Download Class 11 Physics Ch. • Rest: A body is said to be in a state of rest when its position does not change with respect to a reference point. 6. (i) v = u + at. 5 Rotational and Circular Motion Theory Notes ⇛ Class 11 Physics Ch. These are also the class 11 Physics summary that help you read the portion quickly. 10. ar =. Moreover they help you arrive at the class 11 Physics solutions to the chapter-wise questions answers. Download the complete exercises, numerical problems, short questions, and MCQs for Unit 5 from our website. 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 Gravitation, and to encourage them 3 days ago · When a motion of an object denotes changes in the speed of the particle moving along the circular path, it is called non-uniform circular motion. θ = ωit + 1 2αt2 ω2f = ω2i + 2αθ θnth = ω + α 2 (2n − 1) ωrelative = Vrelative rrelative Oct 17, 2023 · JEE Main. Chapter 3: Motion in a Plane. where u is the initial velocity, v is the final velocity, t is the time, a is the acceleration and s is the displacement. Conical Pendulum. 3 days ago · CBSE Class 9 Science Chapter 8 - Motion Revision Notes - Free PDF Download. Page. Uniform circular motion me, rotation aur speed ka angular rate constant hota hai aur non-uniform motion me, rotation ka rate change hote rehta hai. v2 r v 2 r. That is why we have uploaded quality notes of 11th class physics. This causes it to travel in a circular path. These FSc part 1 physics notes include detailed notes of Chapter 5 Circular Motion. It is the area of mechanics where the study of real-world objects at rest is done. Get ready to reach your success in JEE Main 2025 with Laws of Motion Notes that focus on important topics. Feb 3, 2023 · Additionally, many exam questions in physics will require you to apply these formulas, so having a solid understanding of them is crucial for achieving a high score on the exam. Find the magnitude & direction of this force. com/scl/fi/0s2pkl3y8sq51evoez06o/laws-of-motion-part-4 Jan 23, 2024 · Motion Class 9 Notes – Here We have provided summary and revision notes for Class 9 Science Chapter 8. Introduction of Circular Motion in English is available as part of our Physics Class 11 for NEET & Circular Motion in Hindi for Physics Class 11 course. The notes and questions for Notes: Circular Motion, Class 11, Physics have been prepared according to the Class 11 exam syllabus. Jun 30, 2021 · Example 1: A body travels in a semicircular path of radius 10 m starting its motion from point ‘A’ to point ‘B’. The equations developed in this chapter for motion in a plane can be easily extended to the case of three dimensions. The two triangles in the figure are similar. , force which produces the motion. me/sushantsawant9404circular motion class 11 one sho Circular Motion. These notes are your key to achieving high marks in JEE Main exams. Class 11 – Management. Notes By: Bikash Pandeya. Kinetic energy and speed. Let’s learn about the meaning of motion, circular motion, the types of circular motion, its properties, and how to derive a velocity of a body performing the circular motion. 4 days ago · Download Laws of Motion Notes With Important Topics: Score High Marks in JEE Main 2025. Uniform Circular Motion:- Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant. I can qualitatively describe how normal reaction force changes in a vertical circle. The changes that take place in the direction are accounted for by radial acceleration which is given by the given equation. Class 11 Notes . This centripetal force may be provided by friction, tension in a string, gravity etc. State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity. Equations for VCM. (7. 3 equations of motion in circular motion also when angular acceleration is constant. If you’re looking for Chapter 5 “Rotation and Circular Motion” notes of 11th Class Physics in PDF format, you’re in the right place. In its simplest kind, a particle moves in a circular path of constant radius with constant speed. Jun 23, 2020 · For Physics, Chemistry, Biology & Science Handwritten Notes for Class 10th, 11th, 12th, NEET & JEEDownload App: https://play. Class 11 – Science. Ajay Jha / 13 minutes of reading. The speed of the object. 2 SCALARS AND VECTORS In physics, we can Feb 2, 2022 · 6. Now, activities have “to be performed by students. Understanding higher-level physics subjects Dec 13, 2021 · 11th Class Physics Chapter 4 Work & Energy. Δs = rΔθ. Feb 24, 2023 · Angle of friction and repose. org To download notes, click here NOW: will be updated shortlyNEET | NEET Physics | Physics | Class 11 | Class 11 Physics | Physics Class 11 | Unacademy NEET | U Apr 27, 2023 · Motion in a Plane. View PDF CBSE Class 11 Physics Circular Motion Notes. So, if a particle moves in a uniform circular motion: Its speed is constant. Relation between angular displacement and linear displacement: Since, angle = Arc Radius. (iii) s = ut + (1/2)at 2. Work Power and Energy. Circular turnings on roads. 4 m. इस लेख में कक्षा 11 भौतिक नोट्स को रखा गया है। जो NCERT पर आधारित है। इसके अंतर्गत Class 11 physics notes को शामिल किया गया है। इसमें chapter 1 से Apr 19, 2024 · CBSE Class 11 Physics Notes Chapter 3 PDF. Chapter 4: Laws of Motion. Get Physics Circular motion comprehensive notes, detailed Q&As, and past question papers solutions and video tutorials. e. 5 Describe the motion in vertical circle, motion of vehicles on banked surface. 6 Derive the period for conical pendulum. Jul 15, 2018 · Learn the concepts of circular motion, angular velocity and acceleration with Physics Wallah Alakh Pandey, a popular online physics teacher. Answer Aug 19, 2021 · Always change degree into radian. The student knows and applies the laws governing motion in a variety of situations. >. Thus a particle is continuously accelerated. Acceleration: Acceleration is the rate of change of velocity. Velocity changes at every instant. Class 10 – Technical. These chapter-wise revision notes contain key main points only and are also available for free PDF download. If you are a student of class 9 who is using NCERT Textbook to study 4 - Vertical Circular Motion - (with a surface) I can compare the forces on an object at different positions in vertical circular motion. Kinematics of Class 11. An intriguing and one of the most important topics for various government exams after 12th Science, Motion in a plane, which forms an integral part of the Physics syllabus for class 11, covers the basics of 2-d kinematics in a detailed way. As per the question. Welcome to Class 11 Physics chapters from CDC. . (ii) v 2 – u 2 = 2as. The force needed to make something follow a circular path depends on a number of factors: The mass of the object. When a vehicle turns on roads, they travel along a circular arc. Jun 13, 2023 · 📣 For Physics, Chemistry & Bio Handwritten Notes for 11th, 12th, NEET & IITDownload our Apphttps://dhxel. Class 9. Kinematics notes for IIT-JEE. NCERT Solutions Class 11 Physics Chapter 4 – Free PDF Download. • Motion in a plane is called as motion in two dimensions e. All Revision notes for Class 11 Physics have been designed as per the latest syllabus and updated chapters given in your textbook for Physics in Class 11. Find important definitions, questions, notes, meanings May 8, 2022 · We know you are looking for 1st year physics notes of Chapter 5 Circular Motion in PDF to download. 3 Define centripetal force. NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane is one of the important study materials for Class 11 students as it is one of the most scoring chapters in kinematics. It can be broadly divided into the subsequent branches: Statics. We highly recommend that students also study the NCERT solutions for Class 11th. Examples? §6. The physical quantities which are completely specified by their rcular motion is an inst. CBSE Class 11 Physics Notes Chapter 3 Mechanics. Revise Physics chapters and score more with TopperLearning. Contains solved exercises, review questions, MCQs, important questions and chapter overview. Velocity: Velocity is the rate of change of position vector. NEET: Uniform Circular Motion | Physics Class 11 - NEET Jun 22, 2022 · These handwritten notes of Circular motion can be used to prepare for various engineering as well as medical Competitive exams like IIT JEE , NEET UG , COMEDK , BITSAT etc and also for class 11 cbse or state boards. Understanding the concept of banking, used in road design and other scenarios to ensure safe circular motion without skidding. 4. aeroplane, the random motion of gas molecule etc. Aug 31, 2020 · Circular Motion Types: 1. The theories and principles taught in NCERT chapter 8 of motion for class 9 are explained in motion chapter class 9 notes. Mv2r = mω2r M v 2 r = m ω 2 r. Note that centripetal force is the name given to the resultant force: it is not a separate force in the free Indore Sky Space Premium, 1st Floor, Plot No. Normal reaction on a convex bridge. It is a scalar quantity. dropbox. • Dynamics is the branch of physics in which we study the motion of a body by taking into consideration the cause i. distance=πR= 3. Angular Displacement. If the mass of the particle is m, from the 2nd law of motion, you can find that: F = ma F = m a. Physics With AJ is an educational website related to physics, Dec 2, 2021 · circular motion class 11 one shot | short notes for neettelegram channel link Sushant Medico 😊https://t. Download CBSE Class 11 Physics Circular Motion Notes in PDF format. CBSE Class 11 Physics Notes 2023-24 is a comprehensive guide for CBSE Class 11 students. F. Scalar Quantities. PHYSICS. Understanding all the theoretical concepts of the chapter. One activity has been be given in the CBSE Class 11 Physics Practical exam pattern for evaluation now. 4 Derive the expression for centripetal acceleration and use it to solve problems related to centripetal force. Isliye, non-uniform acceleration ke liye, angular acceleration zero nahi hota hai. Dive into the world of Mechanics, Heat, Ray Optics, Electricity and Magnetism, and Modern Physics with confidence, as we present a valuable repository of knowledge to support your learning journey. Chapter 5: Work, Energy, and Power. Bending of cyclist. courses. For the analysis of such motion our reference will be made of an origin and two co-ordinate axes X and Y. ∴ For circular motion. A car is moving on a horizontal curved road with radius 50 m. If it occurs in numerical problems, 1 radian = 180∘ π. 9. These are called scalar quantities. Information about Notes: Circular Motion, Class 11, Physics covers topics like and Notes: Circular Motion, Class 11, Physics Example, for Class 11 2024 Exam. In the case we are discussing here, velocity of the body is different at different points. ‘One activity from any section’ having a weightage of 3 marks will be asked. magnetbrains. Two particles are moving with common speed v such that they are always at a constant distance ' d ' apart and their velocities are always equal and opposite. In chapter notes, there are comprehensive notes of all chapters of FSC part 1 physics. The vector Δ→v points toward the center of the circle in the limit Δt → 0. We shall discuss unifor m circular motion in some detail. youtube. Some Definition Distance: Distance between two points is the length of actual path travelled by the particle. May 12, 2021 · Part 1 of class 11 Physics by NCERT consists of the following chapters: (1) Physical world (2) Units and Measurements (3) Motion in a straight line (4) Motion in a plane (5) Laws of motion (6) Work, Energy and Power (7) System of particles & Rotational Motion (8) Gravitation Don’t get nervous seeing the chapters to cover. The circular motion is a 2D motion in a plane. 5. The velocity rises within the 20 s because a constant force acts on it by unchanging the direction. How many turns are rotated by the disc in 8s? Q. It is an example of non-uniform circular motion. ∴ Angular displacement = Arc PP′ Radius. Calculate the distance and displacement. Dec 19, 2023 · 19 Dec, 2023. Class 11 - Physics - Rotational and Circular Motion - Numerical Problems. (ii) Two dimensional motion. 4 days ago · PDF Summary - Class 11 Physics Motion in a Plane Notes (Chapter 4) 1. Jul 29, 2023 · Uniform Circular MotionClass 11 PhysicsJEE NEET ISC CBSE NCERTPDF of this session: https://www. 2 9. Time period:- It is the time taken by the particle to complete one rotation. Aug 18, 2017 · Study Material and Notes of Ch 8 Motion Class 9th Science. This centripetal force is required to keep the object in a uniform circular motion. Skidding of the vehicle on a level road: When a vehicle makes a turn on a circular path it requires centripetal force. Feb 16, 2020 · ️📚👉 Watch Full Free Course:- https://www. 7 Solve the numerical problem and conceptual question on circular motion. JEE Main. 99 /month! Subscribe. Scalars and Vectors: Some quantities can be described by a unique number. Ans. Although the magnitude of the velocity vector remains constant but the direction of the velocity vector changes direction continuously as shown in Fig. Class 10. Class 9 – Technical. Banking of roads. com/store/apps/details? Circular motion is a motion in which a body travels a definite distance along a circular path. Consider a ball of mass Jun 27, 2022 · JEE Main 2023 (Online) 29th January Morning Shift. Playlist https://www. 25). This knowledge ensures a better understanding of the topics further up in Physics. Jan 19, 2024 · Based on these, motion can be classified as: (i) One dimensional motion. Class 11. It has angular acceleration of –2p rad/s2. This physics note covers both 2D and 3D motion physics. Motion in a Plane Class 11 Notes Physics Chapter 4. Chapter 2: Motion in a Straight Line. 6 days ago · where, a=acceleration, r=radius, v=velocity of the object, ω=angular speed. nce of two dimensional motion. com ️📚👉 Get Notes Here: https://www. actual path traversed by an object is called the distance. (b) Velocity vectors forming a triangle. Average speed: The average speed of an object can be Rotational and Circular Motion – MCQs. Chapter 4 Theory (complete) Chapter 4 Conceptual Questions (complete) 11th Class Physics Chapter 5 Rotational & Circular Motion. The only forces acting on the vehicle are: 1) Weight Mg. The Moon is pulled towards the Earth (at 90 degrees to its direction of travel). store/ or 📞Call / WhatsApp at - 9785944225 Rotational and Circular Motion – Notes. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket The motion of an object moving at uniform acceleration can be described with the help of three equations, namely. 2. 14 x 10 = 31. It can be classified into two types: uniform with constant speed and constant angular rotation rate and non-uniform with changing rotation rate. a r = (Velocity) 2 /radius of motion of the object = v 2 /R. Class 11 Physics Notes Chapter 1 – Measurements Notes Exercise Numerical Problems Important MCQs Chapter 2 – Vectors and Equilibrium Notes Exercise Numerical Problems Important MCQs Chapter 3 – Motion and Force […] May 8, 2022 · These notes are unique in the respect that it has adopted a new curriculum to describe the question and answers. Introduction of Uniform Circular Motion in English is available as part of our Physics Class 11 for NEET & Uniform Circular Motion in Hindi for Physics Class 11 course. r. Normal reaction of the road on a concave bridge. Jan 22, 2021 · This post presents a class note in pdf that covers Projectile Motion, Uniform Circular Motion, and relative motion. Example: Turning of a vehicle in bending roads, motion of satellites arounds planets, motion of planets around sun etc. Class 9 – General. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Mar 26, 2024 · class 11 physics in Hindi medium. Δθ = ΔS r. Non-uniform Circular Motion Definition: If the magnitude of the velocity of the body in circular motion is not constant, then it is called non-uniform 5. Types of Circular Motion: 1) Uniform Circular Motion: The Moon is pulled towards the Earth (at 90 degrees to its direction of travel). Applications of Banking. 5 Rotational and Circular Motion PDF Notes ⇛ Class 11 Physics Ch. 11. A greater mass requires a greater force when the speed and radius are constant. In this context, we will show the syllabus of the basics of physics in a fun and easy-to-understand way. Chapter 6: System of Particles and Rotational Motion. A circular motion is defined as a body movement that follows a circular route. Circular motion uniform ya non-uniform ho sakta hai. google. PDF Link :Shobhit Nirwan Class 11 Physics Laws of Motion Notes PDF. 34 View Question. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Sep 25, 2023 · NEET. 1) Kinematics of Circular Motion. * According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 3. All the notes for Physics. The type of motion in which the body is displaced continuously, but is always confined at a fixed distance from a fixed point is called circular motion. Download more important topics related with notes, lectures and mock test series for NEET Exam by signing up for free. The speed remains constant, but the velocity varies. It is a dimensionless quantity i. Work done on inclined plane. For example, mass, time, distance and speed can be described using a single number. ut ox fw lz mm nn pl wj nd me