Force and Inertia

Force and inertia is a relative concept. This is most simple and interesting topic in physics because it is applicable in day today life. Generally, force is a push or pull and inertia related to any object in its stationary state. This is an overview session on introduction for forces and inertia with simple examples to understand how things work. Next session will focus on Newton’s law of motion which is yet an interesting topic to learn.

Why do we study this force and inertia, what it is going to tell us? The whole world is always in motion. Agree right! Studying motion is a basic need in life and its fundamental law for the big universe too. A force is required to move a stationary body in motion or stop a moving body. Force is always needed to make a move whether it can be in continuous or a short motion. So, force and inertia is literally disturbing a stationary object to make a useful work. In olden days, force and inertia are vital part of one’s life because work is done on the system to do a useful job. When force and inertia are involved there is always a work that is done on the object.

Examples are, push/pull in doors, Hand water pump, water wheels, and pottery making. These all are manmade work which involves force. Nowadays, machines are more, which makes work even simpler like bike, car, fan, and washing machine etc. Remember all these machines or any physical related work will come to rest if no force is applied, literally coming to its inertial state.

• The Greek thinker, Aristotle (384 B.C– 322 B.C.), held the view that if a body is moving, something external is required to keep it moving. According to this view, for example, an arrow shot from a bow keeps flying since the air behind the arrow keeps pushing it. The view was part of an elaborate framework of ideas developed by Aristotle on the motion of bodies in the universe.

• Most of the Aristotelian ideas on motion are now known to be wrong and need not concern us. For our purpose here, the Aristotelian law of motion may be phrased thus: An external force is required to keep a body in motion.

What is the flaw in Aristotle’s argument? The answer is: a moving toy car comes to rest because the external force of friction on the car by the floor opposes its motion. To counter this force, the child has to apply an external force on the car in the direction of motion. When the car is in uniform motion, there is no external force acting on it: the force by the child cancels the force (friction) by the floor. The corollary is: if there were no friction, the child would not be required to apply any force to keep the toy car in uniform motion.

• The opposing forces such as friction (solids) and viscous forces (for fluids) are always present in the natural world. This explains why forces by external agencies are necessary to overcome the frictional forces to keep bodies in uniform motion.

• Now we understand where Aristotle went wrong. He coded this practical experience in the form of a basic argument. To get at the true law of nature for forces and motion, one has to imagine a world in which uniform motion is possible with no frictional forces opposing. This is what Galileo did in his feather and coin experiment. For a falling object (Coin and feather) in vacuum with two different masses will always fall at same time because there is no air resistance. When this experiment is done in the atmospheric condition because of presence of air (mixture of O, N, CO₂) pressure acts as a friction for object to fall at different time based on mass.

The law of inertia:

• Galileo studied motion of objects on an inclined plane (inclination have angle say 45^o).

Objects (i) moving down an inclined plane accelerate, while those

(ii) moving up retard.

(iii) motion on a horizontal plane is an intermediate situation.

Galileo concluded that an object moving on a frictionless horizontal plane must neither have acceleration nor retardation, i.e. it should move with constant velocity (above figure).

• Another experiment by Galileo leading to the same conclusion involves a double inclined plane. A ball released from rest on one of the planes rolls down and climbs up the other. If the planes are smooth, the final height of the ball is nearly the same as the initial height (a little less but never greater). In the ideal situation, when friction is absent, the final height of the ball is the same as its initial height.

• If the slope of the second plane is decreased and the experiment repeated, the ball will still reach the same height, but in doing so, it will travel a longer distance. In the limiting case, when the slope of the second plane is zero (i.e. is a horizontal) the ball travels an infinite distance. In other words, its motion never ceases. This is, of course, an idealised situation (below figure).

The law of inertia was inferred by Galileo from observations of motion of a ball on a double inclined plane.

• In practice, the ball does come to a stop after moving a finite distance on the horizontal plane, because of the opposing force of friction which can never be totally eliminated. However, if there were no friction, the ball would continue to move with a constant velocity on the horizontal plane. Galileo thus, arrived at a new insight on motion that had eluded Aristotle and those who followed him. The state of rest and the state of uniform linear motion (motion with constant velocity) are equivalent.

In both cases, there is no net force acting on the body. It is incorrect to assume that a net force is needed to keep a body in uniform motion. To maintain a body in uniform motion, we need to apply an external force to encounter the frictional force, so that the two forces sum up to zero net external force. Let’s consider most thrilling game that most of us would have experienced. Its water ride, yeah you got it. Galileo’s 1^stand 3^rd (see the figure) motion of the object on inclined plane has helped you to enjoy the water ride, isn’t it? Pendulum is another profound example for the object in motion. In case of pendulum the air is acting as friction and in case of inclined plane experiment the plane itself acts as friction. Pendulum swing and water slide game is satisfied by Galileo’s law of inertia right?!

• To summarise, if the net external force is zero, a body at rest continues to remain at rest and a body in motion continues to move with a uniform velocity. This property of the body is called inertia. Inertia means ‘resistance to change’.