Physics in Depth

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Relative velocity Relative velocity, \(\vec{v_{AB}}\), is the velocity of an object A in the rest frame of an object B. Rest frame of a particle is the coordinate system (frame of reference) in which the particle is at rest . It can be simply defined as, the velocity of an object with respect to another object . Suppose you are in a car A moving north at 90 km/h (with respect to the object in the ground outside). To another man in a car B moving towards north with same speed, you seem to be stationary. Let's discuss this in more detail. For this, we consider following three cases: When the two bodies, body A and body B, are moving in the same direction with velocity \(\vec{v_A}\) and \(\vec{v_B}\) respectively, then the relative velocity of A with respect to B is, \[\vec{v_{AB}}=\vec{v_A}-\vec{v_B}\] So, in above example, it must be clear that for a person in car B moving alongside you with the same speed as yours, you are at rest. When this bodies ar...

Kinematics Rest and Motion When do you declare that some body is in rest or in motion ? Place the book on a table and watch it! Is it in rest? Imagine you being on moon and by some means you could watch your book on your table. Would you again see it in rest? In first case, you would see that the book is in rest but when you are on moon you would see the table, the book and the Earth as a whole in a motion. You are correct in both the cases and it's a good news. Hurray! .It is because rest and motion are not absolute terms but are relative . The book is in rest when you see it from your room because you and the book both do not change position with respect to each other, but it is in motion when you see it from the moon because the moon is moving with respect to the book and book moves with respect to the moon. So, let's set up a definition. If a body changes it's position with respect to the observer ( or reference frame ), then it is said t...

Scalars and Vectors Vector Multiplication Multiplication of a vector by a scalar Let \(\vec{a}\) be the vector and \(\vec{k}\) be the scalar, if we multipy them the result is a vector (i.e., k\(\vec{a}\)). Multiplication of a vector by a vector Vector multiplication are not straightforward as scalar multiplication as they do not follow the ordinary rules of algebra. We can multiply any two vectors in two ways: a. Scalar product and b. Vector product Scalar product / dot product Consider any two vectors \(\vec{a}\) and \(\vec{b}\) inclined at an angle \(\theta\) with each other as in fig. Then we define the scalar product of these two vectors as, \(\vec{a} . \vec{b} = ab cos\theta \) Note that! \(\vec{a} . \vec{b} = \vec{b} . \vec{a}\) Scalar product of any two vectors is always scalar quantity. For example, \(P = \vec{F} . \vec{v}\). Here, force and velocity are vector quantity but the power which is a scalar product of force and velocity is ...

Physical quantities ( measurable quantities ) on the basis of whether they represent magnitude or both magnitude and direction; are broadly classified as scalars and vectors. What are scalars? Scalars are quantities which have magnitude but no direction. A car moving on a road at 80 km/h is said to have a speed of 80 km/h. Speed is a quantity which has no direction but only magnitude, like mass or density or temperature . These quantities are thus the examples of scalars. What are vectors? Vectors are quantities which have both magnitude and direction. A car moving on a road at 80 km/h in north-east direction is said to have a velocity of 80 km/h NE (i.e., north-east ). Velocity is a quantity which has both magnitude and direction, like displacement or force or acceleration . These quantities are thus the examples of vectors. Let's point some of the differences between scalars and vectors. Addition : Scalars obey the ordinary ...

Some tips to correctly solve the short questions: Don't panic : Most of the students find the questions horrible at the very instant they confront the question. Take a deep breath and organize the every possible information.  You will probably find the hint! Read the question carefully : Short questions are very logical. Reading questions carefully will help you to understand the question. As an example take the question " Can a body having constant speed have varying velocity? ". Answer to this is Yes! which can be simply implied from the differences between speed and velocity. Speed is a scalar quantity whereas velocity vary with direction. So speed remaining constant with velocity variable implies that magnitude of both speed and velocity are constant however the direction of body is changing and hence the velocity(Confused?). This is possible in case of circular motion(Think!). Mathematical formulation : Try to aid your answers with mathematical formulati...

Physics is the mathematical formulation of the natural laws. To describe the laws of nature, we need the quantitative description that involves measurement and comparison of physical quantities. To measure a physical quantity we need some standard unit of that quantity. We measure each physical quantity in its own units, by comparison with a standard . The unit is a unique name that we assign to measure of that quantity - for example, meter (m) for the quantity length. The standard corresponds to 1.0 unit of the quantity. The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. [M], [L], [T], [A], etc. are the respective dimensions of mass, length, time and current. Homogeneity of dimensions in an equation : The dimensions of all term in an equation must be identical.i.e. dimension in L.H.S. of an equation is equal to the dimension in R.H.S. of an equation. Limitation of th...

Hello Students, go through these tips and follow all of them to grab the good marks in your board exams. 1. Time management: One of the most important thing in student life is time management skill. Make your daily routine charts and follow it regularly. Most of the students make the daily chart, paste it on their walls and go through it seriously for some days. This will not help! You should be determined and follow the routines everyday. Short naps during daytime might help boost your concentration. Before going to bed, summarize every topics(on your mind) you have gone through in a whole day. 2. Have good food and drink lots of water: Consume the proper healthy diet, juice and water which are sources of high energy and protein. This will help the fast processing of your brain and helps you memorize what you studied. Proteins(meat, fish, eggs, poultry, legumes,dried beans, diary products, etc.) , anti-oxidants(fruits and vegetables),  omega 3(eggs, chicken, oily fish...