Nazarsir.blogspot.com: 1. Laws of motion

Motion of an object :

If the position of an object is changing with respect to its surroundings, then it is said to be in motion.
Otherwise, it is said to be at rest.

Displacement and distance :

Distance’ is the length of the actual path travelled by an object in motion while going from one point to another.
Displacement is the minimum distance between the starting and finishing points.
Even if the displacement of an object is zero, the actual distance traversed by it may not be zero.

Speed and velocity :

The distance travelled in one direction by an object in unit time is called its velocity.
Here, unit time can be one second, one minute, one hour, etc.
If large units are used, one year can also be used as a unit of time.
The displacement that occurs in unit time is called velocity.

The units of speed and velocity are the same. In the SI system, the unit is m/s.
In the CGS system, it is cm/s.
Speed is related to distance while velocity is related to the displacement.
If the motion is along a straight line, the values of speed and velocity are the same, otherwise they can be different.
Velocity is the displacement that occurs in unit time.

Effect of speed and direction on velocity :

• velocity depends on speed as well as direction and that velocity changes by

changing the speed while keeping the direction same
changing the direction while keeping the speed same
changing the speed as well as the direction.

The first scientist to measure speed as the distance /time was Galileo.
The speed of sound in dry air is 343.2 m/s while the speed of light is about 3 × 10 8 m/s.
The speed of revolution of the earth around the sun is about 29770 m/s.

Uniform and non-uniform linear motion :

Uniform linear motion :

If an object covers equal distances in equal time intervals, it is said to be moving with uniform speed.

Non-uniform linear motion :

If an object covers unequal distances in equal time intervals, it is said to be moving with non-uniform speed.
For example, the motion of a vehicle being driven througth heavy traffic.

Acceleration :

The rate of change of velocity is called acceleration.

If the velocity of an object changes during a certain time period, then it is said to have accelerated motion.
An object in motion can have two types of acceleration.

Uniform acceleration.
Non-uniform acceleration.

1. Uniform acceleration :

If the velocity changes by equal amounts in equal time intervals, the object is said to be in uniform acceleration.

2. Non-uniform acceleration :

If the velocity changes by unequal amounts in equal time intervals, the object is say to be non-uniform acceleration.

Positive, negative and zero acceleration :

An object can have positive or negative acceleration.
When the velocity of an object increases, the acceleration is positive. In this case, the acceleration is in the direction of velocity.
When the velocity of an object decreases with time, it has negative acceleration. Negative acceleration is also called deceleration. Its direction is opposite to the direction of velocity.
If the velocity of the object does not change with time, it has zero acceleration.
An object in uniform motion covers equal distances in equal time intervals. Thus, the graph between distance and time is a straight line.

The velocity-time graph shows that :

The velocity changes by equal amounts in equal time intervals.
For all uniformly accelerated motions, the velocity-time graph is a straight line.
For non-uniformly accelerated motions, the velocity-time graph may have any shape depending on how the acceleration changes with time.

Equations of motion using graphical method :

Suppose an object is in motion along a straight line with initial velocity ‘u’.
It attains a final velocity ‘v’ in time ‘t’ due to acceleration ‘a’ its desplacement is ‘s’.
The three equations of motion can be written as

1. v = u + at

This is the relation between velocity and time. This is the first equation of motion

2. S = ut + 1/2 at²

This is the relation between displacement and time. this is Newton’s second equation of motion.

3. v² = u² + 2as

This is the relation between displacement and velocity. this is Newton’s third equation of motion.

Uniform circular motion :

When an object is moving with a constant speed along a circular path, the change in velocity is only due to the change in direction. Hence, it is accelerated motion.
When an object moves with constant speed along a circular path, the motion is called uniform circular motion.
e.g. the motion of a stone in a sling or that of any point on a bicycle wheel when they are in uniform motion.
If an object, moving along a circular path of radius ‘r’, takes time ‘t’ to come back to its starting position, its speed can be determined using the formula given below.

Newton’s laws of motion :

Inertia is related to the mass of the object.
Newton’s first law of motion describes this very property and is therefore also called the law of inertia.

Newton’s first law of motion

Balanced and unbalanced force :

An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it.’
When an object is at rest or in uniform motion along a straight line, it does not mean that no force is acting on it.
Actually there are a number of forces acting on it, but they cancel one another so that the net force is zero.
Newton’s first law explains the phenomenon of inertia, i.e. the inability of an object to change its state of motion on its own.
It also explains the unbalanced forces which cause a change in the state of an object at rest or in uniform motion.
All instances of inertia are examples of Newton’s first law of Motion.

Newton’s second law of motion :

The effect of one object striking another object depends both on the mass of the former object and its velocity.
This means that the effect of the force depends on a property related to both mass and velocity of the striking object.
This property was termed ‘momentum’ by Newton.

Momentum (P) :

Momentum is the product of mass and velocity of an object. P = m v.
Vector quantity.
Has magnitude as well as direction.
Its direction is the same as that of velocity.
In SI system, the unit of momentum is kg m/s, while in CGS system, it is g cm/s.
If an unbalanced force applied on an object causes a change in the velocity of the object, then it also causes a change in its momentum.
The force necessary to cause a change in the momentum of an object depends upon the rate of change of momentum.

Newton’s second law of motion statement:

The rate of change of momentum is proportional to the applied force and the change of momentum occurs in the direction of the force.’

Suppose an object of mass m has an initial velocity u.
When a force F is applied in the direction of its velocity for time t, its velocity becomes v.
The initial momentum of the object = mu, Its final momentum after time t = mv

According to Newton’s second law of motion, the rate of change of momentum is proportional to the applied force.
if the same force is applied on different objects, the change in momentum is the same.
In SI system, the unit of force is newton.

Newton (N) :

The force necessary to cause an acceleration of 1 m/s2 in an object of mass 1 kg is called 1 newton.
1 N = 1 kg × 1 m/s2
In CGS system the unit of force is a dyne.

Dyne:

The force necessary to cause an acceleration of 1 cm/s² in an object of mass 1 gm is called 1 dyne.
1 dyne = 1 g × 1 cm/s2

Newton’s third law of motion :

However, in nature force cannot act alone.
Force is a reciprocal action between two objects. Forces are always applied in pairs.
When one object applies a force on another object, the latter object also simultaneously applies a force on the former object.
The forces between two objects are always equal and opposite.
The force applied by the first object is called action force while the force applied by the second object on the first is called reaction force.
‘Every action force has an equal and opposite reaction force which acts simultaneously.’

Action and reaction Forces :

Action and reaction are terms that express force.
These forces act in pairs. One force cannot exist by itself.
Action and reaction forces act simultaneously.
Action and reaction forces act on different objects. They do not act on the same object and hence cannot cancel each other’s effect.

Law of conservation of momentum :

The magnitude of total final momentum = the magnitude of total initial momentum.
m2 v2 + m1 v1 = m1 u1 +m2 u2
Thus, if no external force is acting on two objects, then their total initial momentum is equal to their total final momentum.
This statement is true for any number of objects.
‘When no external force acts on two interacting objects, their total momentum remains constant. It does not change.’
This is a corollary to Newton’s third law of motion.
The momentum is unchanged after the collision.
The momentum gets redistributed between the colliding objects.
The momentum of one of the objects decreases while that of the other increases. Thus, we can also state this corollary as follows.
‘When two objects collide, the total momentum before collision is equal to the total momentum after collision.’
Backward motion of the gun is called its recoil.
As the mass of the gun is much higher than the mass of the bullet, the velocity of the gun is much smaller than the velocity of the bullet.
The magnitude of the momentum of the bullet and that of the gun are equal and their directions are opposite. Thus, the total momentum is constant.
Total momentum is also constant during the launch of a rocket.