DYNAMICS OF A MATERIAL POINT

DYNAMICS OF A MATERIAL POINT

The first law of motion

Assume that an object is at rest in space, where no force acts upon it, as shown in 1.1.1 figure.

1.1.1 figure. An object at rest in space where no force of gravity acts. Unless a netforce acts on it, it remains at rest. If the object initially were moving with a constantvelocity, it would continue to move with the same constant velocity until itexperiences a net force.

Unless a net force (unbalanced force) acts on it, it remains at rest. If the object initially moves with a constant velocity, it continues to move with the same constant velocity unless it experiences a net force. From this simple experiment, the first law of motion can be inferred, it was stated by Newton more than 3 centuries ago as follows:

If the net force acting on an object is zero

If it is at rest, it will stay at rest.

If it is moving, it keeps on moving at a constant velocity (a constant speed in a straight line)

Inertia

Inertia is the tendency of an object to resist any change in its state of motion.

If an object is at rest, it tends to remain at rest. If the object is inmotion with a constant velocity, it tends to continue to move withthe same velocity, (the same magnitude and direction) The first law is often called the law of inertia because it states that in theabsence of a net force, a body will preserve its state of motion.

The following situations can be discussed in order to understand the law of inertia. If you are in a car which is at rest.

As the car starts moving with an acceleration in a straight line, as shown in1.1.2figure, you can feel the car seat exerting a force on your back which acts to push you forward. Since your body resists the change in its resting state, you experience and feel this force. This force overcomes your inertia and puts you in motion with the same velocity as the car.

1.1.2 figure.As the car begins accelerating, the body resists the acceleration and tends to remain at rest due to inertia.

Let's assume that your car is taking a turn to the right, as shown in 1.1.3 figure. Your body resists the change in the direction of its velocity due to your inertia and tries to keep moving on the straight line. And you feel as though you are being pushed to the left.

1.1.3 figure.As the car takes a turn to the right, a body inside it resists the change in the direction of its velocity due to its inertia and tries to keep moving on the straight line.

Finally if the car breaks suddenly, as shown in 1.1.4 figure, since your body tends to move with the velocity that your car had before breaking, because of your inertia it reacts to this change in its velocity by moving forward.

1.1.4 figure.As the car slows down, a body inside tends to move with the velocity that the car had before breaking, due to its inertia.

Here are some other examples of inertia;

When a hard surface is struck with the back of a hammer, it stops suddenly and the hammer head feels tightened.

When a table cloth, on which there are some plates, is pulled rapidly from under the plates, the plates remain on the table.

When a sheet of kitchen paper is pulled slowly, more and more paper rolls off. However, when a sheet is pulled quickly, it is torn off the roll since the pulling force doesn't have enough time to overcome inertia.

Mass is a Measure of Inertia

Mass is a measure of the response of an object to an external force. The greater the mass of an object, the greater the inertia and the less that object accelerates (changes its state of motion) under the action of a net force. Consider that if a net force causes a 1-kg object to gain an acceleration of , when applied to a 2-kg object, the same net force produces an acceleration of . From this example a relationship can be set-up between the accelerations and the masses of the objects experiencing the same net force.

So the relationship between the masses and their accelerations is

If one of the masses in this equation is known, the unknown mass of an object can be found after the accelerations are measured. Finally, mass is a scalar quantity, it has no direction. It is always positive. It obeys the rules of ordinary arithmetic as other scalar quantities do.