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# Newton’s Laws of Motion

A stationary object remains at rest, and a moving object continues to move at a constant speed and in a straight line unless acted upon by an unbalanced force. The acceleration of an object depends on the mass of the object and the amount of force applied.

## Explain Newton’s Laws of Motion

At one time, matter was known to be anything that occupies space and has mass but the upcoming understanding of Newton’s laws of motion developed a new fact about matter defined it to be anything that occupies space and has its own mass and inertia.

### Newton’s First Law of Motion

According to Newton’s First law of motion, Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state.

In other words, an object at rest remains at rest, or if in motion, remains in motion at a constant velocity that tends to retain its inertia until and unless acted on by a net external force. Newton’s first law of motion is also coming to be considered as the law of inertia.

The external force is the force acting from outside on an object rather than the force from inside of an object. For instance, the force of gravity that exerts on the moon is the external force on the moon. However, the force of gravity that the inner core of the moon exerts on the outer crust of the moon is an example of internal force on the moon. Internal forces within an object can’t cause a change in the overall motion of that object.

#### Inertia

The inherent property of a material body by virtue of which it cannot change, by itself, its state of rest or of uniform motion in a straight line is known as inertia.

#### The Law of Inertia

It was Galileo who first asserted that objects move with constant speed when no external forces act on them.

#### Types of Inertia

Inertia is of three types:

• Inertia of rest
• Inertia of motion
• The Inertia of direction
##### Inertia of Rest

The tendency of a body to retain its position of rest is known as the inertia of rest. It’s the ability of the body to resist any change in its state of rest such as

• A person standing in a bus fall backward when the bus suddenly starts moving because the person initially at rest continues to be at rest even after the bus has started moving.
• When a carpet is beaten with a stick, the dust particles fall vertically downward once they are released and do not move along the carpet before falling off.
• A book on the table or a rock on the ground remains at rest until it is moved by some external agency applying an unbalanced force to displace it.
##### Inertia of Motion

The tendency of a body to remain in its state of uniform motion in a straight line is known as the inertia of motion. For example,

• When a passenger gets down from a moving bus, he tends to fall down in the direction of the motion of the bus.
• An athlete running a race continues to run for some distance even after reaching the finishing line.
• A passenger sitting in a moving car falls forward when the car stops suddenly. The belt used by the car driver is meant to prevent the same when the driver has to apply sudden brakes.
• The swirling of milk in the glass continues even after the stirring is stopped due to the inertia of the motion of the milk inside the glass.
##### Inertia of Direction

The inability of a body to change by itself its direction of motion is known as the inertia of direction. For example,

• The tangentially straight motion of a rock moving in a circular path after being released.
• Sideways falling of a passenger sitting in the bus when the bus takes a sharp turn or goes round on a circular path.
• Protection by an umbrella on a rainy day. The raindrops falling vertically downwards cannot change their direction of motion and so fail to wet us when the umbrella is up.
• Curving of the steering wheel by a car driver when going around on a circular path.

### Newton’s Second Law of Motion

Newton’s 2nd Law of motion states that the rate of change of linear momentum of a body is directly proportional to the applied force and the change takes place in the direction of the applied force.

Newton’s first law states that a body tries to retain its inertia unless an unbalanced force is applied to it. But what happens if the balanced force is applied, is described by Newton’s Second Law of Motion. It states that the force acting on an object is equal to the mass of that object times its acceleration.

Force = mass X acceleration

= m x a

F is force, m is mass and a is acceleration. The relation clearly describes that if one,

• Increases the body by two times, the acceleration possessed by the body also increases by two times.
• Increases the mass by two times, and the acceleration is reduced to half of its initial value with a = F/m.

The force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, the body might appear to speed up, slow down or change its direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

In relation, “F = m x a” both force and acceleration are vector quantities that they both magnitude and direction. The force can be a single force or it can be the combination of more than one force.

#### Momentum

The momentum of the body is the quantity of motion possessed by the body. It is equal to the product of the mass and velocity of the body.

Momentum = mass x velocity

p = m x v

The units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meter/second (kg.m/s). In CGS units it is (g.cm/s).

Being a vector, momentum has magnitude and direction. For example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg.m/s due north measured from the ground.

##### Many particles

The momentum of a system of particles is the sum of their momentum. Suppose two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is

P = p1 + p2

= m1v1 + m2v2

The momenta of more than two particles can be added more generally with the following given below:

p = ∑m1v1

Relation to force

If a force F is applied to a particle for a time interval t, the momentum of the particle changes by an amount.

Δp = F Δ  t

##### Conservation of linear momentum

The second and third laws of motion lead to one of the most important and fundamental principles of physics called the law of conservation of linear momentum. That states: When no external force acts on a system of several interacting particles, the total linear momentum of the system is conserved. The total linear momentum is the vector sum of the linear moments of all the particles of the system.

Suppose, when two particles interact because of the third law, the forces between them are equal and opposite. When the velocities of the particles are u1 and u2 before the interaction, and afterward, they are v1 and v2 then

m1u1 + m2u2 = m1v1 + m2v2

This law remains valid no matter how complicated the force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero (0), so the total change in momentum is zero (0). This conservation law applies to all interactions, including collisions and separations caused by explosive forces.

##### Law of Conservation of Linear Momentum from the second law of motion

Consider an isolated system of n particles. Suppose, n particles have masses m1,m2,m3,…..,mn and are moving with velocities v1,v2,v3,….,vn respectively.

The total linear momentum of the system is

p = m1v1 + m2v2 + m3v3 +…+ mnvn

p = p1 + p2 + p3 +…+ pn

If F is the external force acting on the system, then according to Newton’s second law,

F = dp/dt

For an isolated system,

F = 0

Dp/dt = 0

As the derivative of a constant is zero, so

p = p1 + p2 + p3 +…+ pn = constant

##### Law of Conservation of Momentum

It states that for two objects colliding in an isolated system, the total momentum before and after the collision is equal. This is because the momentum lost by one body is equal to the momentum gained by the other.

### Newton’s third law of motion

Newton’s third law of motion states that in each interaction with every action, there is an equal and opposite reaction.

• It is applicable irrespective of the nature of the forces.
• Action and reaction always act on different objects.
• The forces of action and reaction can’t cancel each other.
• No action can occur in the absence of a reaction.

When two bodies interact with each other, the force exerted by the first body on the second is called action. The force exerted by the second body on the first body is called a reaction. The action and reaction always act on different objects. The third law of motion indicates that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first object. These two forces are always equal in magnitude, but opposite in direction.

#### Example of Newton’s Third Law of Motion

• When a bullet has fired a gun, the gun exerts force on the bullet in the forward direction. This is the action force. The bullet also exerts an equal force on the gun but in a backward direction. This is the reaction force. Due to the large mass of the gun, it moves only a little distance backward by giving a jerk at the shoulder of the gunman or soldier. The backward movement of the gun is known as the recoil velocity of the gun.
• A sailor rowing a boat, a swimmer swimming in the water, a person walking or running on the ground, or the propulsion of a rocket in the air on its way to a space station is an example of the applications of Newton’s third law of motion.
• In a car crash, the action forces are the cars colliding with each other. The reaction force is the force sent back due to collision, which causes car damage.

If two cars are headed straight at each other, they are traveling in opposite directions. When they finally collide, they are traveling in opposite directions if they apply the same amount of force. When they finally collide, if they apply the same amount of force, they experience a reaction of equal magnitude. This causes the destruction of the front of both cars.

Since force is the product of mass and acceleration. If a heavier car i.e., the car with more mass collides with the car having comparatively less mass, there if the two are traveling at the same acceleration, the heavier car is going to experience less damage compared to the lighter car.

FAQs of Newton’s Laws of Motion

What is momentum?

Answer: The momentum of a body is the quantity of motion possessed by the mass. It is equal to the product of the mass (m) and velocity (v) of an object.

Define the impulse of a force

Answer: Impulse is the total effect of a large force that acts for a short time to produce a finite change in momentum. The product of the force (F) and the time (t) for which it acts and is equal to the total change in momentum.

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