Work Energy Theorem

According to this principle, work done by a force in displacing a body, gives the measure of the change in kinetic energy of the body.

When a force does some work on a body, the kinetic energy of the body increases by the same amount. Conversely, when an opposing force is applied on a body, its kinetic energy decreases. The decrease in its kinetic energy is equal to the work done by the body against the retarding force. Thus, work and kinetic energy are equivalent quantities.

Potential Energy -

In among the work energy theorem let us study another type of energy, called the potential energy. Potential energy is the energy that can be associated with the configuration (or arrangement) of a system of objects that exert forces on one another. If the configuration of the system changes, then the potential energy of the system can also change.

One type of potential energy is the gravitational potential energy that is associated with the state of separation between objects, which attract one another via the gravitational force. For example, when Andrey Chemerkin lifted the record breaking weights above his head in the 1996 Olympics, he increased the distance between the weights and earth. The work he did, changed the gravitational potential energy of the weights and earth system because it changed the configuration of the system.

Another type of potential energy is elastic potential energy, which is associated with the state of compression or expansion of an elastic object, say a spring. If we compress or extend a spring, we do work to change the relative locations of the coils within the spring. The result of the work done by our force, is an increase in the elastic potential energy of the spring.Consider the example of two charged particles, A and B. A is positive and B is negative and because of mutual attraction, the particles are accelerated towards each other and the kinetic energy of the system increases. Although, no external force is applied on the system, the kinetic energy changes

Uniform Circular Motion

The uniform circular motion represents the basic form of rotational motion in the same manner as uniform linear motion represents the basic form of translational motion. They, however, are different with respect to the requirement of force to maintain motion.

Uniform linear motion is the reflection of the inherent natural tendency of all natural bodies. This motion by itself is the statement of Newton’s first law of motion : an object keeps moving with its velocity unless there is net external force. Thus, uniform linear motion indicates “absence” of force.

On the other hand, uniform circular motion involves continuous change in the direction of velocity without any change in its magnitude (v). A change in the direction of velocity is a change in velocity (v). It means that an uniform circular motion is associated with an acceleration and hence force. Thus, uniform circular motion indicates “presence” of force.

Let us now investigate the nature of force required to maintain uniform circular motion. We know that a force acting in the direction of motion changes only the magnitude of velocity. A change in the direction of motion, therefore, requires that velocity of the particle and force acting on it should be at an angle. However, such a force, at an angle with the direction of motion, would have a component along the direction of velocity as well and that would change the magnitude of the motion.

Figure 1: A change in the direction of motion requires that velocity of the particle and force should be at an angle.

Change of direction

In order that there is no change in the magnitude of velocity, the force should have zero component along the direction of velocity. It is possible only if the force be perpendicular to the direction of velocity such that its component in the direction of velocity is zero (Fcos90° = 0). Precisely, this is the requirement for a motion to be uniform circular motion.

Figure 2: Force is perpendicular to the direction of velocity.

Uniform circular motion

In plain words, uniform circular motion (UCM) needs a force, which is always perpendicular to the direction of velocity. Since the direction of velocity is continuously changing, the direction of force, being perpendicular to velocity, should also change continously.

The direction of velocity along the circular trajectory is tangential. The perpendicular direction to the circular trajectory is, therefore, radial direction. It implies that force (and hence acceleration) in uniform direction motion is radial. For this reason, acceleration in UCM is recognized to seek center i.e. centripetal (seeking center).

I understand that you still need more help.. keep reading and leave your valuable comments.. i can help you with that........

Motion and Rest Definition

Before we talk about definition on motion and rest let's try to Imagine ourself sitting in a seat while travelling in a moving train. We observe no change in position with respect to the window. There is change of scene when we view through the window. The change of scene indicates that the train is moving.

An object is said to be in motion if it changes its position with respect to its surroundings in a given time.

We know that the window in the cabin is at rest i.e., its position with respect to the walls of the cabin does not change with time.

An object is said to be at rest if it does not change its position with respect to its surroundings.

Have you watched the night sky? We have observed that the position of stars and planets change while you remain stationary. In reality the earth is moving too. Thus, an object which appears to be at rest, may actually be in motion. Therefore, motion and rest are relative terms. To describe the motion of an object we have to specify how its position changes with respect to a stationary object. This is called the frame of reference.

Definition for Motion -

Motion is a state, which indicates change of position. Surprisingly, everything in this world is constantly moving and nothing is stationary. The apparent state of rest, as we shall learn, is a notional experience confined to a particular system of reference.

A building, for example, is at rest in Earth’s reference, but it is a moving body for other moving systems like train, motor, airplane, moon, sun etc

Definition for Rest -

Rest is the term used for time off without any action between sets. Ex. 3 sets for 12 reps means you would complete a movement 12 times then take a rest of 1:30-6 minutes (depending on your goals) then start over for a total of 3 times.

Did you enjoy reading this .. keep reading and leave your comments....

Applications of velocity-time graphs

The variation of velocity with time can be represented graphically to calculate acceleration exactly like we calculated speed from distance-time graph. let me also help you with application of velocity - time graphs

Let us now plot a velocity-time (v- t) graph for the following data.

Velocity in m/s	0	10	20	30	40	50
Time in seconds	0	2	4	6	8	10

If the velocity-time data for such a car were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a changing, positive velocity results in a sloped line when plotted as a velocity-time graph. The slope of the line is positive, corresponding to the positive acceleration. Furthermore, only positive velocity values are plotted, corresponding to a motion with positive velocity.

The velocity vs. time graphs for the two types of motion - constant velocity and changing velocity (acceleration) - can be summarized as follows.

I hope my information on this topic would have helped a lot to understand more on this lesson. Keep reading and leave your valuable comments....

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.