Angular Momentum – Full Discussion

Angular Momentum – Full Discussion

Equilibrium And Types of Equilibriums

Equilibrium And Types of Equilibriums

Equilibrium:- A rigid body is said to be equilibrium if both the linear momentum and angular momentum of the rigid body remain constant with time.

Or we can say that The linear acceleration of the centre of mass of the body would be zero and also the angular acceleration of the rigid body about any axis would be zero. Or we can say that body possesses two equilibria simultaneously or  Conditions for equilibrium

Types Of Equilibrium:-

(i)        Stable Equilibrium: - A body is said to be in stable equilibrium if it tends to regain its equilibrium position after being slightly disturbed and released. In stable equilibrium A body possesses minimum potential energy.

e.g.:- Simple Pendulum, Book kept on a table, as shown in figure

    (ii)         Unstable Equilibrium:- A body is said to be in unstable equilibrium if it gets further                          disturbed from its mean after being slightly disturbed and released. In unstable equilibrium                   a body possesses maximum potential energy.

      e.g.:- Book kept on one edge, a cylinder on inclined plane, image in figure

(iii)       Neutral Equilibrium :- If a body stays in equilibrium position even after being slightly                       disturbed and released. In neutral equilibrium potential energy remains constant Zero.

    e.g.: - A football rolling on ground, image in figure

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Nuclear Energy and Geothermal Energy

Nuclear Energy :-  The energy released when two nuclei of light elements combine with each other to form a heavy nucleus or when a heavy nucleus breaks into two light nuclei is known as nuclear energy.

Basically Nucleus is made of protons and neutrons. And the mass of nucleus must be equal to the sum of mass of protons and mass of neutrons. 

But In realty Mass of nucleus is less then the sum of mass of protons and mass of neutrons this difference in mass is known as mass defect. And this mass defect is reponsible for nuclear energy.

Geothermal Energy :-  We know that earth is made of different layers. And temrature of diffrent layers is different. And we can use this temprature difference to change water into steam and used to produce electrical energy. this temprature difference  is also responsible for hot water springs. 

Dear friends can we explain these two energies in somewhat simpler terms so that students of IXth standard can easily understand these terms ?

Hand Made Notes

Dear Friends

We have uploaded the hand made notes of Unit 1 of CBSE Curriculum and now you can read them or you can download them from the url given below

Hand Made Notes

This is our attempt to help you all. All suggestions are cordially invited.

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Neutral Points

Neutral Points :- It is a point where the magnetic field due to a magnet is equal and opposite to the horizontal component of earth's magnetic field. The resultant magnetic field at the neutral point is zero. 

Does neutral points also exists in Electric and gravitational field also ?

if so how and when ?

Gauss Theorem and its Importance

Gauss's Theorem :-

Gauss Theorem gives a relationship between the total flux passing through any closed surface and the net charge enclosed within the surface.

This theorem states that the total flux through a closed surface is

  times the net charge enclosed by the closed surface.

Mathematically 

Importance of Gauss's Therem :- 

This law or theorem makes it possible to calculate in a simple manner the field strengthens due to many different symmetrical configurations of charge. By a proper choice of gaussian surface we can easily evaluate 

Your's thoughts are cordially invited

Centre of Mass versus Centre of gravity

Does Centre of mass and Centre of gravity is same of different ?

Centre of mass of a body is a point where whole mass of the body may be supposed to be concentrated for describing its translatory motion .

On the other hand centre of gravity is a point at which the  resultant of the gravitational forces on all the particles acts. Or in other words where whole mass of the body may be supposed to act.

On the surface of earth and for the normal dimensions, centre of mass and centre of gravity coinsides. But these two relates to different concepts. For example centre of mass and centre of gravity may be different at greater heights. At mount everest centre of gravity lies below the centre of mass.

Lets reflect on this discussion.

Disscussion on Binary Systems in Nature

Dear Learner Todays Discussion Topic is Binary Systems In Nature

Binary Systems :- Two bodies bound to each other by some force and rotating or orbiting a common centre of mass is called Binary system.

For example:-
1. Binary Stars
2. Diatomic Molecules
3. Earth Moon System etc

Let us explore such system in our daily life. Looking for your valuable comments and suggestions

Pascal's Law:- Demonstration of Hydraulic Lift

Pascals Law

"Pascal's law is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions"

And Hydraulic Lift is an application of the Pascal's Law
A hydraulic lift is basically a force multiplier. It is used to lift heavy objects. 

As shown in the video above a hydraulic lift is consist of two piston of different surface area Let a and A. 
Let we apply a force f on smaller piston then 
pressure on small piston is = f/a
Then 
Pressure on Larger Piston = F/A
According to pascal's law 
Pressure on smaller piston must be transferred to larger piston  i.e.
Pressure on Smaller Piston = Pressure on Larger Piston
f/a  = F/A
F = A*f/a    as A > a  so F  > f  Where A/a is known as multiplier factor

As in this Video a mass of 500g is able to support a mass of 3 kg. In the demostration each block is of 500g. 
and one block is supporting six similar blocks. Have the look and share your views

GGPHYSICS.COM: Todays Discussion:- Einstein's Mass Energy Equival...

GGPHYSICS.COM: Todays Discussion:- Einstein's Mass Energy Equival...: As per logo of the blog Einstein's Mass Energy Equivalence equation is one of the biggest concept in Physics This equation means a l...

Todays Discussion:- Einstein's Mass Energy Equivalence

As per logo of the blog Einstein's Mass Energy Equivalence equation is one of the biggest concept in Physics

This equation means a lot. Can we have a real life meaning of the same. How can a layman can understand this equation ?

Discussion on Work Energy Theorem

Dear Learners from today will  discuss one topic every day on our Blog

And Todays topic is Work Energy Theorem

Statement:-  This theorem states that the work done by the net force on an object is equal to the change in the kinetic energy of the body. 

Mathematically

Final Kinetic Energy - Initial Kinetic Energy = Work Done

Can we state this theorem in a larger sense ?

Worksheet on work power and energy

Worksheet 1 Work, Power and Energy

Q.1  How much work is done on the lawn mower by the person in Figure  if he exerts a constant force of 75.0 N at an angle 35º below the horizontal and pushes the mower 25.0 m on level ground? Convert the amount of work from joules to kilocalories and compare it with this person’s average daily intake of 10,000 kJ (about 2400 kcal ) of food energy. One calorie (1 cal) of heat is the amount required to warm 1 g of water by 1ºC, and is equivalent to 4.184 J , while one food calorie (1 kcal) is equivalent to 4184 J .

Q.2 Suppose a 30.0-kg package on the roller belt conveyor system in Figure is moving at 0.500 m/s. What is its kinetic energy?

Q.3. Suppose that you push on the 30.0-kg package in Figure  with a constant force of 120 N through a distance of 0.800 m, and that the opposing friction force averages 5.00 N. (a) Calculate the net work done on the package. (b) Solve the same problem as in part (b), this time by finding the work done by each force that contributes to the net force.

Q.4. (a) What is the final speed of the roller coaster shown in Figure  if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible? (b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

Q.5. What is the power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s?

Q.6. If a person who normally requires an average of 12,000 kJ (3000 kcal) of food energy per day consumes 13,000 kJ per day, he will steadily gain weight. How much bicycling per day is required to work off this extra 1000 kJ?

Q.7. Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20º with the horizontal. (See Figure below) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.

Q.8. (a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.

Q.9. A hydroelectric power facility (see Figure below) converts the gravitational potential energy of water behind a dam to electric energy. (a) What is the gravitational potential energy relative to the generators of a lake of volume 50.0 km3 ( mass = 5.00×1013 kg) , given that the lake has an average height of 40.0 m above the generators? (b) Compare this with the energy stored in a 9-megaton fusion bomb.

Q.10 (a) How much gravitational potential energy (relative to the ground on which it is built) is stored in the Great Pyramid of Cheops, given that its mass is about 7 × 109 kg and its center of mass is 36.5 m above the surrounding ground? (b) How does this energy compare with the daily food intake of a person?

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WORKSHEET-1- (DIMENSIONAL ANALYSIS)

1. Find the dimensional formulae of the following quantities :

(a) the universal constant of gravitation G     (b) the surface tension S,       

(c) the thermal conductivity k and                  (d) the coefficient of viscosity

2. Find the dimensional formulae of

(a) the charge Q,         (b) the potential V,      (c) the capacitance C, and       (d) the resistance R.

Some of the equations containing these quantities are

Q = It, U = VIt, Q= CV and V = RI; where I denotes the electric current, t is time and U is energy.

3. The SI and CGS units of energy are joule and erg respectively. How many ergs are equal to one  

     joule? Young's modulus of steel is 19 x 10¹⁰ N/m². Express it in dyne/cm². Here dyne is the    

     CGS unit of force.

4. If velocity, time and force were chosen as basic quantities, find the dimensions of mass.

5. Test dimensionally if the equation v² =u² + 2ax may be correct.

6. The distance covered by a particle in time t is given by x = a + bt + ct² + dt³; find the dimensions of     

     a, b, c and d.

6.  If the centripetal force is of the form m^a v^b r^c, find the values of a, b and c.

7. When a solid sphere moves through a liquid, the liquid opposes the motion with a force F. The magnitude of F depends on the coefficient of viscosity η of the liquid, the radius r of the sphere and the speed v of the sphere. Assuming that F is proportional to different powers of these quantities, guess a formula for F using the method of dimensions.

8. The heat produced in a wire carrying an electric current depends on the current, the resistance and the time. Assuming that the dependence is of the product of powers type, guess an equation between these quantities using dimensional analysis. The dimensional formula of resistance is [ML² I^-2T ^-3] and heat is a form of energy.

9.  Taking force, length and time to be the fundamental quantities find the dimensions of (a) density, (b) pressure, (c) momentum and (d) energy.

10. Suppose the acceleration due to gravity at a place is 10 m/s². Find its value in cm/ (minute)².

11. Express the power of a 100 watt bulb in CGS unit.

12. The surface tension of water is 72 dyne/cm. Convert it in SI unit.

13. The volume of a liquid flowing out per second of a pipe of length land radius r is written by a student as  

where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula [ML^–1 T^–1]. Check whether the equation is dimensionally correct.

14. Young’s modulus of steel is 19 x10¹⁰ N/m². Express it in dynes cm². Here dynes are the C.G.S unit       

      of force.

15. The velocity u of water waves may depend on their wavelengthl density of water r and the acceleration due to gravity g. Find relation between these quantities by the method of dimension?

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