In the previous section we saw the 'property of inertia' which was put forward by Galileo. In this section, we will see how Sir Isaac Newton based his studies on that concept.
• The three laws put forward by Newton laid the foundation of Mechanics.
♦ The law of inertia put forward by Galileo was the starting point of newton's works.
■ Newton's first law states that:
Every body continues to be in it's state of rest or of uniform motion in a straight line unless compelled by an external force to act otherwise.
• The law is written in one sentence. But it contains many points.
• We can elaborate it by the following 4 steps:
1. A body can be in any one of the following two states:
♦ The body can be at the state of rest
♦ The body can be at the state of uniform motion in a straight line
2. Which ever be the state, it will continue to be in that state
3. If a 'change in it's state' is required, we must apply an external force on that body
4. As we have seen in the previous section,
♦ If the external forces acting on the body cancel each other, the 'change in state' will not be achieved'
♦ To achieve the 'change in state', there must be a net external force.
■ Now, if a body is at rest, it means that, it has no acceleration
■ If the body is in uniform motion, then also it means that, it has no acceleration
We can all the above information symbolically:
♦ No net force ⇒ The body remains at rest ⇒ No acceleration
♦ No net force ⇒ The body remains at uniform motion ⇒ No acceleration
[The symbol '⇒' stands for 'implies']
• We can connect the first and the third. We get:
♦ No net force ⇒ No acceleration
■ That is., if no net force act on a body, that body will have zero acceleration
• We can write the converse:
If we want a body to have no acceleration, we must not apply a net force on it
From the above discussion, the following points become clear:
■ If we apply a net force on a body, it will experience acceleration
We can write the converse of this also:
■ If a body experiences an acceleration, then a net force is acting on the body
Let us see some practical applications of the above information:
Example 1:
1. A child pulls a non-electric toy car by a string
See fig.5.3(a) below:
• Let the toy car move with uniform velocity
• Then the car experience zero acceleration
2. Based on Newton's First law, we can write:
■ No net force is acting on the car
3. But we must analyse the situation and write the reason for 'no net force and hence no acceleration '
• We see that the child is applying a force through the string. Even then we say that, net force is zero.
• So what happened to the force applied through the string?
• The answer is that, the 'force applied through the string' is canceled by 'another force in the opposite direction'.
4. This 'another force' is the frictional force which is acting at the interface between the tyres and the floor
• The child tries to pull the car forward
• The frictional force oppose this forward motion
5. The two forces obviously have opposite directions
• So if the two forces are equal in magnitude, they will cancel each other
• If the child's pull is greater in magnitude, then the car will move with acceleration.
■ We can give the inference by writing the three statements below:
1. The car is observed to be moving with uniform velocity.
2. So the net external force on it must be zero
3. By Newton's first law, we conclude that, the following two forces are equal in magnitude but opposite in direction:
(a) Force applied by the child
(b) Frictional force at the interface between the wheels and the floor
■ We must not write the inference in this way:
1. The following two forces are equal in magnitude but opposite in direction:
(a) Force applied by the child
(b) Frictional force at the interface between the wheels and the floor
2. The two forces cancel each other
3. So we observe the car to be moving with uniform velocity
■ Why are we not able to write the inference by the above three statements?
Ans: When beginning to solve a problem, we may not be knowing all of the following items:
(i) The forces which are acting
(ii) The magnitudes of the forces
(iii) The directions of the forces
• It is by the 'application of Newton's first law', that we make an inference:
The frictional force is equal in magnitude but opposite in direction to the applied force
Example 2:
1. A book rests on a table. See fig.5.3(b) above
• It has no motion at all
• Then the book has zero acceleration
2. Based on Newton's First law, we can write:
■ No net force is acting on the book
3. But we must analyse the situation and write the reason for 'no acceleration and hence no net force'
• In example 1 above, we see a 'visible force' which is applied through a sting.
• We asked: What happened to that force?
• And we found the answer
• But here, we see no 'visible force'
• We are inclined to conclude that:
The case of 'no net force' need not be considered here. Because no force is acting
4. But on all objects on earth, the gravitational force is acting.
• Because of this force, the book will be pulled down wards.
• The magnitude of this force is equal to 'W', the weight of the book
5. So now we have to consider 'net force'
• We have a force 'W' acting on the book
• Yet we see no acceleration
• What happened to 'W'?
• The answer is that, 'W' is cancelled by 'another force in the opposite direction'.
6. This 'another force' is the reaction 'R' exerted by the table
• It is easy to see that, if the table is not present to provide 'R', the book will fall
• The 'W' tries to pull the book downwards
• The 'R' opposes this downward motion
■ We can give the inference by writing the three statements below:
1. The book is observed to be at rest.
2. So the net external force on it must be zero
3. By Newton's first law, we conclude that, the following two forces are equal in magnitude but opposite in direction:
(a) The weight W of the book
(b) The reaction R exerted by the table
■ We must not write the inference in this way:
1. The following two forces are equal in magnitude but opposite in direction:
(a) The weight W of the book
(b) The reaction R exerted by the table
2. The two forces cancel each other.
3. So we observe the book to be at rest
■ Why are we not able to write the inference by the above three statements?
Ans: When beginning to solve a problem, we may not be knowing all of the following items:
(i) The forces which are acting
(ii) The magnitudes of the forces
(iii) The directions of the forces
• It is by the 'application of Newton's first law', that we make an inference:
The Reaction R is equal in magnitude but opposite in direction to the weight W
■ We see that the property of inertia put forward by Galileo is contained in Newton's first law
• We experience inertia in many day to day situations
Let us see an example. We will write it in steps:
1. Consider a person standing inside a bus
• Initially, the bus is at rest
• When the bus starts to move forward, the person tends to fall backwards
2. This can be explained as follows:
• The feet are in contact with the floor.
• When the floor moves forward the feet (due to inertia), would want to stay at rest.
• The feet would not want to move with the floor.
3. But the friction (between the feet and the floor) will not allow the feet to stay at rest.
• It will carry the feet forward.
4. This motion of the feet should carry the entire body forward.
• But the human body is somewhat flexible. It is not a rigid object.
• So the upper parts will not experience the same motion of the feet.
5. The upper parts like to stay at rest, and somewhat succeeds in doing so.
• But the feet is not present straight below to carry the upper part. It has moved forward.
• So the person falls back
6. The opposite happens when the bus stops.
• The feet comes to stop due to friction.
• The upper parts tend to continue being in the state of motion.
• But the feet has stopped moving. There is no feet straight below to carry the upper part.
• So the person falls forward
• The three laws put forward by Newton laid the foundation of Mechanics.
♦ The law of inertia put forward by Galileo was the starting point of newton's works.
■ Newton's first law states that:
Every body continues to be in it's state of rest or of uniform motion in a straight line unless compelled by an external force to act otherwise.
• The law is written in one sentence. But it contains many points.
• We can elaborate it by the following 4 steps:
1. A body can be in any one of the following two states:
♦ The body can be at the state of rest
♦ The body can be at the state of uniform motion in a straight line
2. Which ever be the state, it will continue to be in that state
3. If a 'change in it's state' is required, we must apply an external force on that body
4. As we have seen in the previous section,
♦ If the external forces acting on the body cancel each other, the 'change in state' will not be achieved'
♦ To achieve the 'change in state', there must be a net external force.
■ Now, if a body is at rest, it means that, it has no acceleration
■ If the body is in uniform motion, then also it means that, it has no acceleration
We can all the above information symbolically:
♦ No net force ⇒ The body remains at rest ⇒ No acceleration
♦ No net force ⇒ The body remains at uniform motion ⇒ No acceleration
[The symbol '⇒' stands for 'implies']
• We can connect the first and the third. We get:
♦ No net force ⇒ No acceleration
■ That is., if no net force act on a body, that body will have zero acceleration
• We can write the converse:
If we want a body to have no acceleration, we must not apply a net force on it
From the above discussion, the following points become clear:
■ If we apply a net force on a body, it will experience acceleration
We can write the converse of this also:
■ If a body experiences an acceleration, then a net force is acting on the body
Let us see some practical applications of the above information:
Example 1:
1. A child pulls a non-electric toy car by a string
See fig.5.3(a) below:
 |
| Fig.5.3 |
• Then the car experience zero acceleration
2. Based on Newton's First law, we can write:
■ No net force is acting on the car
3. But we must analyse the situation and write the reason for 'no net force and hence no acceleration '
• We see that the child is applying a force through the string. Even then we say that, net force is zero.
• So what happened to the force applied through the string?
• The answer is that, the 'force applied through the string' is canceled by 'another force in the opposite direction'.
4. This 'another force' is the frictional force which is acting at the interface between the tyres and the floor
• The child tries to pull the car forward
• The frictional force oppose this forward motion
5. The two forces obviously have opposite directions
• So if the two forces are equal in magnitude, they will cancel each other
• If the child's pull is greater in magnitude, then the car will move with acceleration.
■ We can give the inference by writing the three statements below:
1. The car is observed to be moving with uniform velocity.
2. So the net external force on it must be zero
3. By Newton's first law, we conclude that, the following two forces are equal in magnitude but opposite in direction:
(a) Force applied by the child
(b) Frictional force at the interface between the wheels and the floor
■ We must not write the inference in this way:
1. The following two forces are equal in magnitude but opposite in direction:
(a) Force applied by the child
(b) Frictional force at the interface between the wheels and the floor
2. The two forces cancel each other
3. So we observe the car to be moving with uniform velocity
■ Why are we not able to write the inference by the above three statements?
Ans: When beginning to solve a problem, we may not be knowing all of the following items:
(i) The forces which are acting
(ii) The magnitudes of the forces
(iii) The directions of the forces
• It is by the 'application of Newton's first law', that we make an inference:
The frictional force is equal in magnitude but opposite in direction to the applied force
Example 2:
1. A book rests on a table. See fig.5.3(b) above
• It has no motion at all
• Then the book has zero acceleration
2. Based on Newton's First law, we can write:
■ No net force is acting on the book
3. But we must analyse the situation and write the reason for 'no acceleration and hence no net force'
• In example 1 above, we see a 'visible force' which is applied through a sting.
• We asked: What happened to that force?
• And we found the answer
• But here, we see no 'visible force'
• We are inclined to conclude that:
The case of 'no net force' need not be considered here. Because no force is acting
4. But on all objects on earth, the gravitational force is acting.
• Because of this force, the book will be pulled down wards.
• The magnitude of this force is equal to 'W', the weight of the book
5. So now we have to consider 'net force'
• We have a force 'W' acting on the book
• Yet we see no acceleration
• What happened to 'W'?
• The answer is that, 'W' is cancelled by 'another force in the opposite direction'.
6. This 'another force' is the reaction 'R' exerted by the table
• It is easy to see that, if the table is not present to provide 'R', the book will fall
• The 'W' tries to pull the book downwards
• The 'R' opposes this downward motion
■ We can give the inference by writing the three statements below:
1. The book is observed to be at rest.
2. So the net external force on it must be zero
3. By Newton's first law, we conclude that, the following two forces are equal in magnitude but opposite in direction:
(a) The weight W of the book
(b) The reaction R exerted by the table
■ We must not write the inference in this way:
1. The following two forces are equal in magnitude but opposite in direction:
(a) The weight W of the book
(b) The reaction R exerted by the table
2. The two forces cancel each other.
3. So we observe the book to be at rest
■ Why are we not able to write the inference by the above three statements?
Ans: When beginning to solve a problem, we may not be knowing all of the following items:
(i) The forces which are acting
(ii) The magnitudes of the forces
(iii) The directions of the forces
• It is by the 'application of Newton's first law', that we make an inference:
The Reaction R is equal in magnitude but opposite in direction to the weight W
■ We see that the property of inertia put forward by Galileo is contained in Newton's first law
• We experience inertia in many day to day situations
Let us see an example. We will write it in steps:
1. Consider a person standing inside a bus
• Initially, the bus is at rest
• When the bus starts to move forward, the person tends to fall backwards
2. This can be explained as follows:
• The feet are in contact with the floor.
• When the floor moves forward the feet (due to inertia), would want to stay at rest.
• The feet would not want to move with the floor.
3. But the friction (between the feet and the floor) will not allow the feet to stay at rest.
• It will carry the feet forward.
4. This motion of the feet should carry the entire body forward.
• But the human body is somewhat flexible. It is not a rigid object.
• So the upper parts will not experience the same motion of the feet.
5. The upper parts like to stay at rest, and somewhat succeeds in doing so.
• But the feet is not present straight below to carry the upper part. It has moved forward.
• So the person falls back
6. The opposite happens when the bus stops.
• The feet comes to stop due to friction.
• The upper parts tend to continue being in the state of motion.
• But the feet has stopped moving. There is no feet straight below to carry the upper part.
• So the person falls forward
In the next section, we will see how Newton's second law.
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