If you find Physics mind boggling here is the thread you need to follow to get your physics concepts cleared.
Prof. Ashish Arora, (@prof.ashish.arora on PaGaLGuY), Head of of Allen Career Institute, Jaipur, explains physics concepts that are important for the JEEs.
Pulley constrained motion is the most common constrained motion from where we start developing understanding of constrained motion. Thorough understanding of Pulley Constrained Motion helps in solving variety of problems in the topic of Laws of Motion.
There are two ways to solve the problems of Pulley Constrained Motion -
(i) By observation on in-extensible strings of constant lengths and
(ii) By method of Virtual Work
Lets discuss both methods -
(i) By observation on in-extensible strings of constant lengths
In this method by moving any one block of system we carefully observe how the length of string is being shifted from one side of pulley to other side and analyze the motion of movable pulley as well. In case of a moving pulley, it pulls double the length of string from either side whereas in case of a fixed pulley change in length in string on one side is compensated by change in length of string on its other side.
For better understanding see the video - https://youtu.be/EL1QT4WcgY4
Some examples on this are -
(ii) By Method of Virtual Work
In this method we consider total work done by ideal string to be zero in displacement of blocks of system. As we know ideal string is massless and massless passive bodies can never gain or supply energy so total work done by all strings of system on all the blocks of system must be equal to zero.
To analyze the same we consider different displacements of the blocks and calculate work done by strings on blocks by taking scalar product of string tension to the displacement of the block and equate total work to zero. This equation gives us the relation of displacements of all the blocks of the system which in turn gives us the relation in velocity and accelerations.
All the above examples can be solved also by using this method of virtual work also.
To understand advance Illustrations on the above concept, see these videos -
JEE Advanced 2015 Paper was a surprising one for many aspirants with several new factors which are seen first time in JEE-
1. no single choice correct questions,
2. -2 negative marking and off beat lengthy questions
3. unbalanced set of questions in 3Hrs.
Although paper pattern was far different from expectation, it should not have put any impact on competition as the paper was for all aspirants appearing in exam.
This years paper analysis reveals lot of new factors which students must incorporate in their JEE preparation and plan their preparation strategy in alignment to these factors.
To understand about these important factors see the analysis video link below. Video link is - https://youtu.be/KPCtkAROL8g
Free Body Diagram is a pictorial method to solve problems based on Newton's Second Laws of motion where motion of a moving body is analyzed under various forces including tension in a string, normal contact force, friction and other external forces acting on the block.
In this method we apply all forces acting on a body considering it as a point object and represent all forces by drawing arrows at the point. After drawing all arrows at the point object we resolve all forces in two mutually perpendicular directions, one along the motion direction of body and other normal to it.
Now we write equations of Newton's Second Law of Motion in both perpendicular directions and solve these equations to get the required motion parameters of the body.
To understand basics of Free Body Diagram, see the video https://youtu.be/LrJzCKtpbDQ
To understand basics of Normal contact force and how it is used in FBD, see the video https://youtu.be/WYrFKJXZaiU
To understand basics of Tension force applied by a string and how it is used in FBD, see the video https://youtu.be/QE_uKOPIhMM
For various Applications of Newton's Second Law of Motion pl see the videos -
Wedge Constrained Motion is an important constrained motion which is used in framing variety of problems related to Newton's Laws of Motion. Understanding Wedge constrained motion also helps in handling complex problems on applications of Newton's Second Law.
Wedge constrained motion describes the motion of a block over another block of the shape of a prism or a cuboid called a wedge which slides over a smooth or rough surface. In such types of system of blocks we start our analysis by assuming the motion of first block relative to wedge and then if wedge is also moving then we consider its motion relative to the surface on which it moves.
Unlike to the case of pulley constrained motion, here students are advised to analyze the motion only by observation which is the best way to deal with such types of problems.
Misconception: Many times in problems of wedge-block systems, students apply the method of Virtual Work and it deviates the final result of the problem because in case of relative motion of block over wedge work done by normal contact force is non-zero so this method of Virtual Work is not advisable in solving the problems of wedge constrained motion whereas it work well with pulley constrained motions.
To understand the basics on how to handle wedge constrained motion in simple wedge-block systems and understanding the relations of acceleration of blocks, see the video given below -
To understand further on wedge constrained motion, pl follow the examples given below -
There are several problems which are framed on combination of Wedge and Pulley constrained motion of blocks. Once you develop the basic understanding of wedge constrained motion, next step is to practice on the problems based on combination of both wedge and pulley constrained To develop understanding on the mixed cases of pulley and wedge constrained motion, see the below illustrations -
Free Body Diagram is a pictorial method to solve problems based on Newton's Second Laws of motion where motion of a moving body is analyzed under various forces including tension in a string, normal contact force, friction and other external forces acting on the block.
In this method we apply all forces acting on a body considering it as a point object and represent all forces by drawing arrows at the point. After drawing all arrows at the point object we resolve all forces in two mutually perpendicular directions, one along the motion direction of body and other normal to it.
Now we write equations of Newton's Second Law of Motion in both perpendicular directions and solve these equations to get the required motion parameters of the body.
To understand basics of Free Body Diagram, see the video https://youtu.be/LrJzCKtpbDQ
To understand basics of Normal contact force and how it is used in FBD, see the video https://youtu.be/WYrFKJXZaiU
To understand basics of Tension force applied by a string and how it is used in FBD, see the video https://youtu.be/QE_uKOPIhMM
For various Applications of Newton's Second Law of Motion pl see the videos -
When a body slides over another body its motion can be analyzed in two ways. Either in the reference frame of ground or in the reference frame of lower body over which the upper body is sliding. In second case depending upon the state of motion of lower body the free body diagrams of upper body will change.
Understanding Pseudo Force: If the lower body is accelerating then relative to lower body, upper body will accelerate in opposite direction and it experience a force causing this acceleration with respect to lower body (as seen by an observer on lower body). This force we call Pseudo Force acting on upper body as it is not an actual force but it appears which causes the acceleration with respect to the lower body.
So whenever a problem related to motion of a block over another block is analyzed, it can be easily handled in the reference frame of lower block by considering Pseudo Force on the upper block.
To understand it see the video - https://youtu.be/fjDMfvpMGB0
Whenever a problem is there on situation of a block sliding over another moving block, its analysis if done by using the concept of Pseudo Force, the solution will be easier and short.
To develop applications on how to use Pseudo Force in a variety of problems see the examples given in below videos -
Friction due to surface roughness always opposes relative motion or tendency of relative motion between bodies in contact. Whenever friction acts it always acts on the two bodies in opposite direction. But friction is different when bodies are at rest and tend to slide or these are sliding.
So lets first discuss about the basics of friction and its classification in the below videos. Friction and its Classification - https://youtu.be/pzijTUmAe2c
Depending upon the state of motion there are three ways in which Friction is considered - Static friction, Limiting Friction and Kinetic friction. See this video to understand these in detail - https://youtu.be/YCz8sh8rEoo
Common mistake of students in Problems of friction: While solving problems involving friction, you need to be very careful in drawing free body diagrams of bodies as friction always acts on two bodies in contact in opposite directions. When students draw FBD of sliding bodies in the given situation of problem, they draw an arrow representing friction on one body and miss it on another body as psychologically they feel they have considered friction somewhere. So always remember to draw friction in FBD twice. Both on different bodies in their independent FBDs in opposite direction.
How we use the concept of friction in various problems using free body diagram(FBD), see the examples explained in below videos - https://youtu.be/fkijA9jjTeg
The concept of friction is very important in variety of of problems involving concept of Newton's Laws of Motion. Whenever a block is placed over the rough surface of another block then it is also important to analyze the condition on external effects under which the upper block starts sliding.
Several problems are framed on such condition. When a body is subjected to external forces and if it is at rest relative to the surface on which it is placed then the friction acting at the contact would be static friction. If external force is increased the magnitude of static friction between bodies will increase and as it approaches limiting value, bodies will start sliding.
This concept can be easily applied when the lower block is at rest but when both blocks are in motion, we need to be very careful while solving the equations of Laws of Motion as the analysis is now done relative to lower block.
See the video below on how to apply the concept in finding the condition of sliding when a block is moving over another block - https://youtu.be/VOEWcZiJHLg
To apply the logic in various situations, see the examples explained in below videos -
Misconception: While solving problem of finding condition of sliding of a block over another the most common mistake students do by simply calculating static friction and equate it with limiting friction in the reference frame of lower block and ignore the motion of lower block. Due to acceleration of lower block the static friction on upper block changes. If you analyze the problem in the reference frame of lower block which is accelerating always consider the Pseudo Force on the upper block relative to lower block.
There can be variety of problems which can be framed on this concept of sliding of a body over another body.
See the below advance illustrations to develop a thorough understanding on application of this concept.
From early grades we study energy is the ability to do work by a body or an agent. When an agent does work by applying force, it is said that amount of energy equal to work will be transferred to the body on which work is done. Whenever work is done transfer of energy takes place. The body which supplies energy is considered as agent who is doing work and its work is taken positive and another body on which work is done gains energy and the its work is taken negative.
Calculation of Work: By the fundamental method studied in early grades we calculate work by product of force and displacement of point of application of force.
See this video on work and its calculation - https://youtu.be/WEriI0hK0lc
Sometimes applied force varies with position of body then to understand how to calculate work by a
variable force see this video - https://youtu.be/5fenCV_tUHw
Always remember that no matter how logical and advance the problem is, we will use always the fundamental way to calculate the work.
Many times students feel for advance problem there are some advanced ways for work calculations. In further study we will see some more cases but the fundamental method explained above will always be applicable.
See below examples on work calculations -
We are studying from childhood which indicates the capacity of doing work by an agent or any body and work is the transfer of energy from one body/agent to another. Both energy and work are measured in units of joule as SI unit and erg as CGS unit. As we've discussed and understood work, we'll now talk about energy and its types.
There are many physical situations in almost every domain of physics where energy transfer and energy transformations are used and in all such situations in one or many ways work is involved.
Problems based on such situations are handled by concept of Work-Energy theorem.
To understand basics of Energy and its types follow the video - https://youtu.be/JUb6_f9XnnY
Conservative and Non-Conservative Fields : When work is done by a force, it is equal to the transfer of energy from one body/agent to another. Now based on type of force field doing the work, energy is either used by the body on which work is done or it may be dissipated to a non-recoverable form. Understanding force field is one of the most important section we need to go through before proceeding to work energy theorem.
Pl see the video below for fundamental understanding of force fields https://youtu.be/S2_JB_qwgls
Potential Energy Stored in a Spring : Springs are used in various problems related to physical situations involving Work and Energy. When a spring is compressed or elongated it stores energy in form of potential energy which can be retrieved for doing work again.
We can discuss the same through this video - https://youtu.be/ZTw9zf8s2rE
Work-Energy theorem is a fundamental basis of handling problems involving physical situations in several domains of physics where energy transformations take place. Whenever some work is done by a force it is equal to the decrease in energy of the agent who is doing the work and same amount of energy increases in the body/agent on which work is done. If work is done on/by a rigid body, it is equal to change in kinetic energy of body if only mechanical energy is involved as rigid body cannot store potential energy in its own. This is the basis we use for application of Work-Energy Theorem while using it for rigid bodies.
To understand basics of Work-Energy Theorem follow the video - https://youtu.be/uvNZu1yy9Co
Relation in Potential Energy and Force: We know that Potential Energy is a characteristic of Conservative force fields only where no dissipation of energy take place. Whenever some work is done on or by an external agent in a conservative force field, this work is always equal to change in stored potential energy of the force field. Based on this concept we can deduce the relation in potential energy and force.
See the video for details - https://youtu.be/QBM0U-6vkzk
To understand the same with applications of the above logic, see the example videos below -
Work-Energy theorem is very useful in analyzing situations where a rigid body moves under several forces. As we know that a rigid body cannot store potential energy in its lattice due to rigid structure, it can only possess kinetic energy. Thus the work done by any force acting on a rigid body is equal to the change in its kinetic energy. This is the basis of work energy equation for rigid bodies.
To analyze motion of a rigid body in such situation, see the video:
In variety of cases when a spring is connected to body then in case when a spring is compressed or elongated, it absorbs energy and stores in form of elastic potential energy which is due to the negative work done by spring on the attached body.
So work done by spring will always be subtracted from body energy if it absorbs energy and will be added to body energy if it releases energy.
To understand similar cases, pl see the example videos below - https://youtu.be/CeoxRfJe0zg
For general situations which involves friction and other cases, more example videos are given below -
In a conservative force field the relation in force and potential energy is given as F = - dU/dx so if at a point in conservative force field there can be three general conditions for which force on a particle becomes zero.
Case - I : When U = Constant
In this case the U vs x curve will be a section of horizontal straight line in which there is no change in potential energy if body is displaced slightly on this section where potential energy is constant. Thus the gradient of potential energy or Force on particle is zero and such a position for particle is called the state of neutral equilibrium when it does not experience any force on displacement in a force field.
Case - II : When U is Maximum
In this case the tangent to U vs x curve will have zero slope and again force on particle at this position will be zero but when the particle is displaced from this position in either direction, particles potential energy decreases so particle will experience a force in the direction away from the maximum potential energy position. Such a position as force is zero it is in equilibrium but if particle is displaced, it tend to move away from this position so it is called the state of unstable equilibrium.
Case - III : When U is Minimum
In this case also the tangent to U vs x curve will have zero slope and again force on particle at this position will be zero but when the particle is displaced from this position in either direction, particles potential energy increases so particle will experience a force in the direction toward the minimum potential energy position. Such a position as force is zero it is in equilibrium but if particle is displaced, it tend to move toward this position so it is called the state of stable equilibrium.
Lets understand the Concept of Equilibrium through this video https://youtu.be/_tUvRNxuYkg
To understand the application of Equilibrium concept follow the Example Videos below -
Power is the rate at which energy is supplied or gained by a system of body/bodies. Power of a system can be expressed in two ways
Average Power
Instantaneous Power.
Average Power: It is defined for a given period of time as the ratio of total work done by a system to the total time taken in doing the work. For a rigid body the work done will be change in its kinetic energy and for a conservative force field it is equal to its change in potential energy as we already discussed earlier.
Instantaneous Power: It is the rate at which energy is supplied or gained at an instant of time in the process of energy transfer. Mathematically it can be expressed as time derivative of work done or that of kinetic energy in case of a rigid body.
Lets understand the Concept of Power and its calculation through the video https://youtu.be/WUou1gkDppc
To understand the application of Power in different physical situations, follow the Example Videos given below - https://youtu.be/Z8nJJisv7Ws
Circular Motion is an angular motion in which distance of a particle in motion remain constant from a fixed point, the center of the circular trajectory of the motion.
Basic Properties of Circular Motion of a particle are -
Angular Displacement,
Angular Velocity and
Angular Acceleration which are related in same manner as linear motion displacement, velocity and acceleration are related.
Angular Velocity is the time derivative of angular displacement and Angular Acceleration is the time derivative of angular acceleration. Similar to linear motion angular acceleration can also be given as product of angular velocity and the derivative of angular velocity with respect to angular displacement.
For Uniform Angular Acceleration we can also use the Angular Speed Equations for angular motion in similar manner to linear speed equations.
See the video to understand the basics of Circular Motion and its properties - https://youtu.be/a0JK0-Gmais
To understand the relation in linear and angular properties of circular motion, see the video - https://youtu.be/nMNP_f3YSRw
For detailed understanding of Angular Acceleration, see the video - https://youtu.be/xnrPiJDHp6M
For the application of the above explained concepts, follow the solved examples in the videos given below -
When a body moves in two dimensional motion, its velocity magnitude and direction both may change. Change in velocity is always due to some acceleration in body, which is caused by an external force.
When a force acts on a body in two dimensional motion, the direction of force is very important in deciding what changes will happen in the body velocity.
The force component along the tangential direction to trajectory of body causes the change in magnitude of velocity and the acceleration due to this is called Tangential Acceleration and the force component which acts along the normal to trajectory of body causes the change in direction of velocity and acceleration due to this component of force is called Normal Acceleration which is also termed as Centripetal Acceleration.
To understand it thoroughly, see the videos below - https://youtu.be/E6fNMDOD2kk
Based on the understanding of Tangential and Normal Acceleration which are the two rectangular components of a force, there are many physical situations where these concepts are extremely helpful.
See the examples below to follow the applications of these concepts.
First we will discuss a basic Horizontal Circular Motion of a Conical Pendulum which is a specific type of circular motion of a simple pendulum. When the bob of a suspended simple pendulum moves in a horizontal uniform circular motion, the string of the bob moves on the surface of cone, such a system is called Conical Pendulum.
Analysis of motion of a Conical Pendulum is given here in video -https://youtu.be/y-o4o4KQSmA
As the circular motion is an accelerated motion then in the reference frame of an observer moving along the body in circular motion the body will experience a Pseudo Force due to the normal acceleration in observer.
This Pseudo Force will act in radially outward direction on body as seen by observer as observers acceleration (centripetal acceleration) is in radially inward direction. This Pseudo Force on body we call Centrifugal Force. But on applying Centrifugal Force we need to consider body to be at rest as it is seen in the frame of an observer who is also moving in circular motion along with the body.
To analyze the Centrifugal Force in detail, see the video - https://youtu.be/1PKHmVPeiLc
For detailed understanding and applications on Horizontal Circular Motion, see the example videos below - https://youtu.be/MGDQjK99fz0
When a pendulum bob is projected in such a way that it moves in a circular motion on vertical plane, its speed as well as tension in string continuously vary due to effect of gravity. Analysis of this motion is very important as on many such situations varieties of problems are framed.
When a pendulum bob is imparted an initial velocity at its bottom most stable position, it starts following the vertical circular motion and as it goes up due to negative work of gravity its kinetic energy decreases and the decrease in kinetic energy decreases the centrifugal force acting on it in rotating reference frame due to which string tension also decreases.
Depending upon the initial velocity of projection when it goes up in the upper part of circular trajectory, its tension may become zero and it may no longer continue the circular motion.
See this video for analysis of this vertical circular motion - https://youtu.be/9hivNCWgwt8
So for different initial velocities of projection there can be different cases of motion of the bob which we can study one by one. See this video for the different cases of projection of the pendulum bob in vertical circular motion -https://youtu.be/htiFN9EHCgA
In different cases we have seen that if initial velocity of projection is not sufficient, the string may slack in upper half of circular trajectory and bob may leave the trajectory and follow the parabolic trajectory of projectile motion.
If instead of a string we use a light rod in making the pendulum, it will never be slack and the bob will always follow the circular path but may return if its velocity become zero anywhere in the motion.
See this video for this motion analysis of bob -
First we will discuss a basic Horizontal Circular Motion of a Conical Pendulum which is a specific type of circular motion of a simple pendulum. When the bob of a suspended simple pendulum moves in a horizontal uniform circular motion, the string of the bob moves on the surface of cone, such a system is called Conical Pendulum.
Analysis of motion of a Conical Pendulum is given here in video - https://youtu.be/y-o4o4KQSmA
As the circular motion is an accelerated motion then in the reference frame of an observer moving along the body in circular motion the body will experience a Pseudo Force due to the normal acceleration in observer. This Pseudo Force will act in radially outward direction on body as seen by observer as observers acceleration (centripetal acceleration) is in radially inward direction. This Pseudo Force on body we call Centrifugal Force. But on applying Centrifugal Force we need to consider body to be at rest as it is seen in the frame of an observer who is also moving in circular motion along with the body.
To analyze the Centrifugal Force in detail, see the video - https://youtu.be/1PKHmVPeiLc
For detailed understanding and applications on Horizontal Circular Motion, see the example videos below -