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).

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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.

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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.

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