Physics of Vectors & Motion Mechanics (7.0 hrs | 63 lessons)
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- What are Vectors and Scalars
- Vector Components and Unit vectors (I,j and k)
- Dot Product and Cross Product
- What are Position and Displacement Vectors
- Velocity, speed and displacement
- Instantaneous Velocity and Acceleration
- 3 Equations of motion
- Area under a velocity -time curve
- Projectile Motion: Why Vertical Velocity changes, Horizontal does not
- Projectile Motion: Why a Parabolic Path? Why Max Range at 45 degree
- Circular Motion: What is Centripetal Force
- This course assumes you have studied Physics in standard 10 or High School
How can you become really good at topics like Vectors and mechanics of motion in 1,2 and 3 dimension in physics?
With over 2700 enrollments and 4.7 star rating, these 62 lessons will help and guide you to become good at these topics
This topic covers the concept of mechanics, vectors, displacement and velocity and acceleration in two and three dimensions. Projectile motion and circular motion is explored in depth. Motion in 2 and 3 Dimension requires use of vectors to describe the motion of the bodies. Vector notation is used in most places to understand and appreciate the close dependence of this kind of motion on vectors.
Like most topics in Physics, this too requires deep understanding of concepts to make sense of numerical problems and their solutions.
Learn physics faster and better - It is not difficult! It just requires a some time, focus and a good teacher :)
Once you are enrolled in the course, all you need a note book and a pen to get cracking on these topics
What are Vectors and Scalars
Vector Components and Unit vectors (I,j and k)
Dot Product and Cross Product
What are Position and Displacement Vectors
Velocity, speed and displacement
Instantaneous Velocity and Acceleration
3 Equations of motion
Area under a velocity -time curve
Projectile Motion: Why Vertical Velocity changes, Horizontal does not
Projectile Motion: Why a Parabolic Path? Why Max Range at 45 degree
Circular Motion: What is Centripetal Force
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Vectors form the foundation of several topics in Physics but dealing with them can be confusing. This lesson starts from the basics and builds up on what are vectors and how you add and subtract them. Includes use of unit vectors, cross product, dot product etc. Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is velocity, the magnitude of which is speed.
Understanding vector components or vector resolution and how you can add the components to form vectors is essential to solve higher level problems in various topics of Physics. So vectors can sometimes be very confusing and the best way of dealing with them is to put them in a coordinate system
A unit vector is any vector that has a magnitude of "one". It can point in any direction. Such vectors are usually used to specify directions and therefore they do not have any dimension like other vectors (e.g. m/s for velocity).
The unit vectors in the positive direction of x, y and z axis are labelled as i,j and k respectively with a small hat on top. They are used to express other vectors by combining the magnitudes of those vectors with i,j and k. Example a vector V having magnitude “a” in x direction and “b” in y direction can be written as V = ai + bj (V needs to have an arrow on top while i and j should have cap as per the proper notation)
Vector Multiplication usually takes 3 forms - (a) Dot Product (b) Cross product and (c) Vector multiplied by a scalar.
Watch this video for easy understanding of this topic. Multiplication of a vector by a scalar changes the absolute value of the vector, but the direction remains the same. The scalar value alters the magnitude of the vector. The scalar in a way increases or reduces the vector. The dot product of two vectors is the value of one vector multiplied by the projection of the second onto the first one.
The cross product of two vectors is basically the area of the parallelogram between them in value terms. The symbol used to represent this multiplication is a diagonal cross and that is why it is termed "cross product". This product has value and direction.
Finding Cross Product of 2 vectors and the direction of the resultant vector is easy, provided one understands the simple cork screw rule. In this lesson, find how cross product is calculated and how it differs from dot product.
The cross product of 2 vectors f and g is defined in three-dimensional space only and is expressed as f × g. Cross product a × b is defined as a vector c that is perpendicular to both a and b, and has direction given by the cork screw rule or the right-hand rule and a magnitude is the area of the parallelogram that the vectors make
Average velocity, speed and displacement as concepts help us work around motion. "Motion in a straight line" is one of the most interesting topics in Physics. In this tutorial, we will cover the concepts and see how these can be applied to solve some difficult numerical problems
Instantaneous velocity and acceleration as concepts are quite often misunderstood. They require an understanding of basic level calculus. While average velocity is measure over a period of time, instantaneous velocity is measured at an instant in time. In this lesson you will understand what it is and when it is to be used.
Motion in 2 & 3 Dimension starts with good understanding of what are position and displacement vectors. Once you understand the 2 concepts, it becomes much easier to understand the topic that may include different kind of motions like projectile or circular motion.
Projectile motion involves velocity in vertical and horizontal direction. It is important to understand that the two are independent of each other. Solving problems becomes much easier with this simple understanding.
It is a wonder that Projectile Motion takes a Parabolic Path and 45 degree is the angle that offers maximum range. Study the math behind the physics of the topic. In this video, understand the concept of range and angle of projection for maximum displacement in horizontal direction
The problem has a boatman having a displacement vector that takes him to the wrong destination. It is required to find the vector that takes him to the intended destination. This problem requires us to identify the three vectors i.e. the actual displacement vector, intended displacement vector and the required vector to reach the destination.
Skillful addition of vectors to form the equation helps in solving the problem
The problem has a vector placed in the 3rd Q. We need to establish the components of the vector. This requires taking the proper angle that the vector makes with the X axis. Vector problems often require beginners to identify the location of the vector and then establish the angle and therefor eventually the sign of the vector components
Solution to the problem requires conversion of 3 displacement vectors into i,j,k notation and finding the resultant vector by adding them.
Often the vectors are expressed as displacement in meters. Converting them to i,j,k form requires carefully putting them on the cartesian plane and finding the sum
The problem has vector C = sum of vector A and vector B, further magnitude of C = that of vector A. The information is to be used to find vector C FOR ONLINE TUTORIALS BY ME: Please write to firstname.lastname@example.org Please also indicate (a) Your class (11th, 12th, High School etc.) (b) Preferred time slot for tutorial PDF COPY OF PROBLEM, WRITE TO: email@example.com MORE PROBLEMS & SOLUTION: https://goo.gl/HXz94V SUBSCRIBE TO "THE SCIENCE CUBE": https://goo.gl/eKiXTp FACEBOOK: https://www.facebook.com/The-Science-... The problem requires skillful use of expressing vectors in an equation form to solve for the unknown vector.
The problem combines the use of i, j and k vector notation and the parallelogram method to solve the problem. This requires placement of vectors on the coordinate plane and converting the vectors into i,j,k notation and establishing a relationship between them. alternately, the parallelogram method of finding vectors can also be adopted. Finding the right angle that a vector makes with the X axis is also very important
How do you find the area of the triangle between two vectors?
Given a graph that plots the velocity vs. time for a runner, find displacement of the runner
What would be the velocity of a packet being carried up by a parachute when it is dropped and hits the ground. Important to understand that the initial velocity vector of the packet would be same as that of the balloon. Therefore use of appropriate sign for velocity as a vector is essential for putting in the equation of motion that is used.
What are displacement and velocity of two diamonds, dropped from a building at different times. At what time are they 10 m apart? The problem requires careful plotting of information on a diagram and deriving the equations that connect velocity, time and displacement under gravity to give the solution
A parachutist falls under gravity and then the chute opens. What are velocity, displacement at various times. This problem tells us how the direction of acceleration is opposite the direction of fall and positive despite being a deceleration. Also, how the equations of motion are wisely used to solve the problems
Trajectory of a bullet is also parabolic in nature, it is however not noticeable due to high initial velocity. This problem tries to find the angle a bullet should be shot above the horizontal such that the parabolic nature of the trajectory is neutralized and the bullet hits the bulls eye.
Projectile Motion problems can often be solved by way of "time reverse" motion method. This is a concept better understood by way of a solving a problem. In this example, we have an object thrown from top of a building and it takes a certain trajectory. Given the velocity and angle at which it hits the ground, find the angle of throw and the initial velocity.
This problem finds the angle at which an archer fish should spit a water projectile to hit an insect at the max height of the projectile of the spit ball. The angle needs to be more than the straight line angle that the fish makes with the insect.