Newton's second law for uniform circular motion

Newton's Law of Motion is also a co related motion to uniform circular motion. Whenever an object experiences uniform circular motion there will always be a net force acting on the object pointing towards the center of the circular path. This net force has the special form , and because it points in to the center of the circle, at right angles to the velocity, the force will change the direction of the velocity but not the magnitude.

It's useful to look at some examples to see how we deal with situations involving uniform circular motion.
Example -
let me try to help you with an example on newton's second law of motion for uniform circular motion. Identical objects on a turntable, different distances from the center. Let's not worry about doing a full analysis with numbers; instead, let's draw the free-body diagram, and then see if we can understand why the outer objects get thrown off the turntable at a lower rotational speed than objects closer to the center.

In this case, the free-body diagram has three forces, the force of gravity, the normal force, and a frictional force. The friction here is static friction, because even though the objects are moving, they are not moving relative to the turntable. If there is no relative motion, you have static friction. The frictional force also points towards the center; the frictional force acts to oppose any relative motion, and the object has a tendency to go in a straight line which, relative to the turntable, would carry it away from the center. So, a static frictional force points in towards the center.

Summing forces in the y-direction tells us that the normal force is equal in magnitude to the weight. In the x-direction, the only force there is is the frictional force.

The maximum possible value of the static force of friction is

As the velocity increases, the frictional force has to increase to provide the necessary force required to keep the object spinning in a circle. If we continue to increase the rotation rate of the turntable, thereby increasing the speed of an object sitting on it, at some point the frictional force won't be large enough to keep the object traveling in a circle, and the object will move towards the outside of the turntable and fall off.

Why does this happen to the outer objects first? Because the speed they're going is proportional to the radius (v = circumference / period), so the frictional force necessary to keep an object spinning on the turntable ends up also being proportional to the radius. More force is needed for the outer objects at a given rotation rate, and they'll reach the maximum frictional force limit before the inner objects will.

Have you understood the importance of newton's law of motion for circular motion. keep reading ... In the next lesson .. lets learn on Uniform Motion and Non-uniform Motion

Uniform Circular Motion

In this lesson .. let me help go through circular Motion and its importance along with sample problem.
The revolution of moon around the Earth and the revolution of an artificial satellite in a circular orbit round the Earth are examples of circular motion.
Consider a particle moving with constant speed along the circumference of a circle of radius R in the anticlockwise direction. The time taken by the particle to go round the circle once is called the time period of the particle and is denoted by the letter T.
Examples on Uniform Circular Motion -
Below are the following examples on uniform Circular Motion.
Example 1 - Twirling an object tied to a rope in a horizontal circle. (Note that the object travels in a horizontal circle, but the rope itself is not horizontal). If the tension in the rope is 100 N, the object's mass is 3.7 kg, and the rope is 1.4 m long, what is the angle of the rope with respect to the horizontal, and what is the speed of the object?

As always, the place to start is with a free-body diagram, which just has two forces, the tension and the weight. It's simplest to choose a coordinate system that is horizontal and vertical, because the centripetal acceleration will be horizontal, and there is no vertical acceleration.

The tension, T, gets split into horizontal and vertical components. We don't know the angle, but that's OK because we can solve for it. Adding forces in the y direction gives:

This can be solved to get the angle:

In the x direction there's just the one force, the horizontal component of the tension, which we'll set equal to the mass times the centripetal acceleration:

We know mass and tension and the angle, but we have to be careful with r, because it is not simply the length of the rope. It is the horizontal component of the 1.4 m (let's call this L, for length), so there's a factor of the cosine coming in to the r as well.

Rearranging this to solve for the speed gives:

which gives a speed of v = 5.73 m/s.

I hope example was more explanatory and easy to understandable as well. Did you enjoy reading this and was it really helpful do you?.. Do you still require more help on Physics like this... Don't worry.. i can help you on like this... keep reading and may be in the next lesson let us learn on Graphical Representation of Uniform Motion.

Simple Harmonic Motion

In our daily life we come across various kinds of motions. You have already learnt about some of them, e.g. rectilinear motion and motion of a projectile. Both these motions are non-repetitive. We have also learnt about uniform circular motion and orbital motion of planets in the solar system. In these cases, the motion is repeated after a certain interval of time, that is, it is periodic.
Simple Harmonic Motion -
let me help you go through on simple harmonic motion. Let us consider a particle vibrating back and forth about the origin of an x-axis between the
limits +A and –A as shown in Figure. In between these extreme positions the particleA particle vibrating back and forth about
the origin of x-axis, between the limits +A and –A. moves in such a manner that its speed is
maximum when it is at the origin and zero when it is at ± A. The time t is chosen to be
zero when the particle is at +A and it returns to +A at t = T. In this section we will describe
this motion. Later, we shall discuss how to achieve it.
In general, a body may vibrate under the action of restoring forces not directly proportional to displacement. However, such complicated motions can be considered as suitable combination of two or more simple harmonic motions. Many types of motion, such as the oscillation of a pendulum, can be considered approximately simple harmonic, provided the amplitude is small. It must be noted that acceleration in Simple Harmonic Motion is not a constant and hence, the equations of motion of bodies with uniform acceleration cannot be applied in this case.
I hope my information on simple harmonic motion was helpful to you. keep reading .. i can help understand on all your doubts on Physics help. Let me also try to help you more on Uniform Circular Motion.

Gas Laws - Boyle's Law

Gas laws were always been an important aspect in all terms of physics. This has been explained by kinetic-theory-of-gases as well as Boyle's Law. Let me help you go through basically on Gas laws - Boyle's Law.
First let me help you understand what is Gas laws - The study of behaviour of gases has led to the formulation of a few important generalisations called as Gas Laws.
Boyle's Law -
Robert Boyle proposed this law in the year 1662, giving the relationship between pressure and volume of given mass of a gas at constant temperature. This law states that volume (V) of a given mass of gas is inversely proportional to the pressure (P) at constant temperature.

Let me also try to explain on mathematical terms.

Example - The density of water is 1000 kg m–3. The density of water vapour at 100 °C and 1 atm pressure is 0.6 kg m–3. The volume of a molecule multiplied by the total number gives ,what is called, molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and
pressure.

Answer - For a given mass of water molecules, the density is less if volume is large. So the
volume of the vapour is 1000/0.6 = /(6 ×10 -4 ) times larger. If densities of bulk water and water molecules are same, then the fraction of molecular volume to the total volume in liquid
state is 1. As volume in vapour state has increased, the fractional volume is less by the
same amount, i.e. 6×10-4.

I hope this was more helpful to you. May be in the next lesson .. let me help you go through on Physical Properties of Water keep reading and leave your valuable comments.

Universal Law of Gravitation

Law of Gravitation is an basic fundamental lesson for every one to learn. Gravitation force is also an important lesson to study. I would like to share my knowledge on universal law of gravitation.
Introduction to universal law of gravitation
The Law of Universal Gravitation explains the phenomenon of gravitation. Gravitation is the reason for the fall of the bodies, why the Earth and other planets revolve around the Sun, it is the reason behind the ties and other very well stated phenomena.
Illustration of Universal Law of Gravitation -
Let me also help you understand gravitation force with the help of sample illustration.
Gravitational force on point mass m1 is the
vector sum of the gravitational forces exerted by m2, m3 and m4. The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if
the entire mass of the shell is concentrated at the centre of the shell.
I hope with this illustration on universal law of gravitation you got an good idea on gravitation. If you still need more help on Physics then keep reading.. i may also help you understand on law of conservation of energy

NEWTON’S THIRD LAW OF MOTION

NEWTON’S THIRD LAW OF MOTION
I hope you all enjoyed in learning about Newton's law of motion on Newton's first law and second law of motion. Hear i will help you understand more on newton's third law of motion.
The second law relates the external force on a body to its acceleration. What is the origin of the external force on the body ? What agency provides the external force ? The simple answer in Newtonian mechanics is that the external force on a body always arises due to some other body.
Equal and Opposite Force
The forces on the space-shuttle are similar to the forces in a collision between two tennis balls. When the balls collide, they are propelled in opposite directions. The rockets of the space-shuttle force burning gases downward through the exhaust vents. In response to these downward forces, the shuttle system moves upward. The motion of the space-shuttle demonstrates Newton's third law of motion. When one object exerts a force upon a second object, the second object exerts an equal and opposite force upon the first object. The third law of motion states that every action has an equal and opposite reaction. You can see equal and opposite forces interact when you blow up a balloon and release it, it moves in the opposite direction. The force propelling the balloon is equal and opposite to the force of the air leaving the balloon
Have you got an hang on newton's law of force. Keep reading .. let me also share with you on an Experiment on Newtons Third Law .

Summary on Work, Energy and Power

Summary on Work, Energy and Power -
Hear is an important topic i have to share and debate with you all. Summary on Work, Energy and Power is an important think in our day today life. In physics, however, the word ‘Work’ covers a definite and precise meaning. Somebody who has the capacity to work for 14-16 hours a day is said to have a large stamina or energy. We admire a long distance runner for her stamina or energy. Energy is thus our capacity to do work. In Physics too, the term ‘energy’ is related to work in this sense, but as said above the term ‘work’ itself is defined much more precisely. The word ‘power’ is used in everyday life with different shades of meaning. In karate or boxing we talk of ‘powerful’ punches.

Law of conservation energy is also an important think to debate on. Let us see what is actually taking place in the following examples

• Steam engine- Here the coal burns and the heat due to the combustion of coal converts water into steam and the expansive force exerted by the steam on the piston of the engine moves the locomotive
• Hydroelectric power plant- Here water stored in a reservoir is made to fall on turbines which are kept at a lower level and which in turn are connected to coils of an a.c. generator

Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another.

I hope this was more interesting and meaningful to you all. I am very sure that i have enlightened your mind to learn more on Physics. No problem i will help in all the topics on Physics Help. Keep reading and leave your comments .........

NEWTON’S SECOND LAW OF MOTION

We just learned about newton's first law of motion. In this lesson let me take you through and help you understand about newton's second law of motion.
The first law refers to the simple case when the net external force on a body is zero. The second law of motion refers to the general situation when there is a net external force acting on the body. It relates the net external force to the acceleration of the body.
Momentum -
Momentum, P of a body is defined to be the product of its mass m and velocity v, and is
denoted by p: p = m v
Momentum is clearly a vector quantity. The following common experiences indicate the
importance of this quantity for considering the effect of force on motion.
• Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded
truck) are parked on a horizontal road. We all know that a much greater force is needed to
push the truck than the car to bring them to the same speed in same time. Similarly, a
greater opposing force is needed to stop a heavy body than a light body in the same time,
if they are moving with the same speed. This will also help you on laws of motion.
• If two stones, one light and the other heavy, are dropped from the top of a building, a
person on the ground will find it easier to catch the light stone than the heavy stone. The
mass of a body is thus an important parameter that determines the effect of force
on its motion.
Force not only depends on the change in momentum but also on how fast the change is brought about. A seasoned cricketer draws in his hands during a catch, allowing greater time for the ball to stop and hence requires a smaller force.

I hope you got a hang up on newton's second law of motion. Probably on the next lesson let me help you understand on newton's third law of motion.

KINETIC THEORY OF GASES

kinetic Theory of Gases -
Boyle, Newton and several others tried to explain the behavior of gases by considering that gases are made up of tiny atomic particles. The actual atomic theory got established more than
150 years later. Kinetic theory of Gases explains the behavior of gases based on the idea that the gas consists of rapidly moving atoms or molecules. This is possible as the inter-atomic forces, which are short range forces that are important for solids and liquids, can be neglected for gases.
The kinetic theory of matter was developed in the nineteenth century by Maxwell, Boltzmann and others. It has been remarkably successful. It gives a molecular interpretation of pressure and temperature of a gas, and is consistent with gas laws and Avogadro’s hypothesis. It correctly explains specific heat capacities of many gases. It also relates measurable properties of gases such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses. This chapter gives an introduction to kinetic theory.
Kinetic theory of gases is based on the molecular picture of matter. A given amount of gas is a collection of a large number of molecules (typically of the order of Avogadro’s number) that
are in incessant random motion.
I hope you got a brief knowledge with these explanation. keep reading i can surprise you with some more of explanation on Physics help.

NEWTON’S FIRST LAW OF MOTION

I am very sure everyone might have learned about Newton's Law of Motion. Hear i will take you through briefly on newton's first law of motion.
Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.The state of rest or uniform linear motion both
imply zero acceleration. The first law of motion can, therefore, be simply expressed as: If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body and this will also help you understand on law of motion gravity.
Two kinds of situations are encountered in the application of this law in practice. In some
examples, we know that the net external force on the object is zero. In that case we can conclude that the acceleration of the object is zero. For example, a spaceship out in interstellar space, far from all other objects and with all its rockets turned off, has no net external force acting on it. Its acceleration, according to the First Law, must be zero. If it is in motion, it must continue to move with a uniform velocity.

I hope you got a fair knowledge on newton's first law of motion. In the next lesson i will help you go through newton's second law of motion. keep reading and do give you me your comments.

MOTION IN A STRAIGHT LINE

Introduction to Motion in a Straight line
Physics is an interesting subject to study and Motion in a Straight line is one among the topics.
Let me share with you few interesting facts on Motion
Motion is common to everything in the universe. We walk, run and ride a bicycle. Even when we are sleeping, air moves into and out of our lungs and blood flows in arteries and veins. We see leaves falling from trees and water flowing down a dam. Automobiles and planes carry people from one place to the other. The earth rotates once every twenty-four hours and revolves round the sun once in a year. The sun itself is in motion in the Milky Way, which is again moving within its local group of galaxies.

Displacement
It is useful to define another quantity displacement as the change in position. Let x1 and x2
be the positions of an object at time t1 and t2. Then its displacement, denoted by Δx, in time Δt = (t2 - t1), is given by the difference between the final and initial positions : Δx = x2 – x1
Displacement has both magnitude and direction. Such quantities are represented by
vectors. You will read about vectors in the next chapter. Presently, we are dealing with motion
along a straight line (also called rectilinear motion) only.
lets try to explain Motion with one simple example

Question - A car is moving along a straight line, say OP in Fig. 3.1. It moves from O to P in 18 s and returns from P to Q in 6.0 s. What are the average velocity and average speed of the car in going (a) from O to P ? and (b) from O to P and back to Q ?
Answer -

This is how we understand on Motion in a straight line. Do you still need more help on Physics ?

Basics Forces in Nature

In this lesson lets try to learn more on the basics Fundamental Forces in Nature and its types

We all have an intuitive notion of force. In our experience, force is needed to push, carry or
throw objects, deform or break them. We also experience the impact of forces on us, like when
a moving object hits us or we are in a merry-ground.

In the macroscopic world, besides the gravitational force, we encounter several kinds
of forces: muscular force, contact forces between bodies, friction (which is also a contact force
parallel to the surfaces in contact)

At the present stage of our understanding,we know of four fundamental forces in nature,
which are described here :

• Gravitational Force
• Electromagnetic Force
• Strong Nuclear Force
• Weak Nuclear Force
• Towards Unification of Forces

Nature of Physical law
Physicists explore the universe. Their investigations, based on scientific processes,
range from particles that are smaller than atoms in size to stars that are very far away. In
addition to finding the facts by observation and experimentation, physicists attempt to discover
the laws that summarize (often as mathematical equations) these facts.

Reflection and Refraction

Reflection and Refraction
In this topic lets try to examine what is all about Reflection and Refraction.

• Reflection-

Reflection is the returning, or "bouncing" of a wave off of a surface which resists that kind of wave. When it reflects, it always does so at the exact same angle it came in at. If you shine a light directly at a 90 degree angle, it will come directly back at a 90 degree angle. If you shine it 45 degrees to the left, it will exit 45 degrees to the right. The angle at which the light comes in is called the angle of incidence, while the angle at which it exits is called the angle of reflection. This observation is called the scientific law of reflection, which states that the angle of incidence is equal to the angle of reflection. A reflection coming off a smooth surface is sharp, because the waves are allowed to return "intact", without being disturbed. But, if the reflective surface is not a smooth one, what is called diffuse reflection occurs. Because the surface is not smooth, different parts of the light hit the surface in different places at different depths and different times. This results in a mostly blurred image, which is why rough, grainy surfaces do not reflect images well.

• Refraction

Refraction is the change in direction of a wave when it passes into a new substance. The reason the light changes direction or "bends" is because each different substance has it's own effect on the speed of light within itself. Every substance has an optical density, this number, called the substance's index of refraction, is how well light passes through it, the higher the density, the harder time light has moving through it. This number can be determined in two ways, first, the index can be found by taking the ratio of the speed of light in a vacuum (3x106 km/s) and the speed of light in the substance. It can also be found by taking the ratio of the sine of the angle of incidence and the angle of refraction, similar to the angles mentioned above. This equation is called Snell's Law.