**About the Author**:

**Mickheal Navani**is a Young physicists, and holds a BSc in Physics from Green land University India. He writes for majority of science blogs. Follow him @ [email protected]

**Preamble**

**Apart from kinematics, dynamics**

deals with motion and the force that causes motion. Wikipedia defines dynamics as a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to

*kinematics*, which studies the motion of objects without reference to its causes. Thus,

dynamics is defined as the aspect of mechanics under which are we study about

the system of forces acting on a body that is in motion.

Sir Isaac Newton had at a time carried out an elaborate work on motion

and the force that caused motion. Its

findings were summarized in what has now come to stay as the celebrated

Newton’s law of uniform motion. Thus,

having a clear understanding of force and motion requires an adequate

understanding of these laws.

and the force that caused motion. Its

findings were summarized in what has now come to stay as the celebrated

Newton’s law of uniform motion. Thus,

having a clear understanding of force and motion requires an adequate

understanding of these laws.

**Inertia and the Newton First Law of**

Uniform Motion

Uniform Motion

The first law has much to do about a quantity known as inertia. When a body is at rest, it has its tendency

to continue to remain in the state of rest.

This tendency is inertia. In the

same way, object in motion also has its tendency to continue its motion on a

straight line. This is also inertia.

to continue to remain in the state of rest.

This tendency is inertia. In the

same way, object in motion also has its tendency to continue its motion on a

straight line. This is also inertia.

Using the above, the inertia of a body hence is defined as the tendency

of a body at rest to continue to be in union on a straight line. The mass of a body is the measure of its

inertia ie the greater the mass of a body, the greater the force required to

change its states of rest or uniform motion.

The property of matter is called the inertia mass.

of a body at rest to continue to be in union on a straight line. The mass of a body is the measure of its

inertia ie the greater the mass of a body, the greater the force required to

change its states of rest or uniform motion.

The property of matter is called the inertia mass.

Newton first law of uniform motion is the summary of the above

explanation. The law states as follows

every object will continue in its present state of rest or uniform motion in a straight line , unless it is been acted upon by an

external force. The above provided the

force that causes motion, just like the concept of heat and temperature

explanation. The law states as follows

every object will continue in its present state of rest or uniform motion in a straight line , unless it is been acted upon by an

external force. The above provided the

force that causes motion, just like the concept of heat and temperature

**Newton Second law of Uniform Motion**

While the first law admits that

force causes motion, the second law sets out to describe the force that causes

motion. In doing this , a quantity known

as momentum is used. The mass of a body

and its velocity ie

force causes motion, the second law sets out to describe the force that causes

motion. In doing this , a quantity known

as momentum is used. The mass of a body

and its velocity ie

p= mass

x velocity

x velocity

where p is the momentum

Note

however that momentum can change since the velocity that is used in defining

momentum can change as well. Thus there

are

however that momentum can change since the velocity that is used in defining

momentum can change as well. Thus there

are

(I)

Initial momentum (p)

Initial momentum (p)

(II)

Final momentum (p)

Final momentum (p)

Where

**p1**= mu and**P2**

= mv, u and v are the initial and final velocity respectively. If m is the mass in kilogram (kg) and

u and v are the velocities in m/s then momentum will be kgm/s. Note that the

fact that momentum and change in momentum is used in describing forces that cause motion.

This as well has been explained by the Newton’s law of uniform motion which states as

follow:

u and v are the velocities in m/s then momentum will be kgm/s. Note that the

fact that momentum and change in momentum is used in describing forces that cause motion.

This as well has been explained by the Newton’s law of uniform motion which states as

follow:

F

α

α

__ê____p__ t

Since

– p1

Since

__ê__p p2– p1

(change

of momentum)

of momentum)

F α p2 – p1

t

F α

mu – mv

mu – mv

t

F α

m(v-u) (since v-u =

acceleration)

m(v-u) (since v-u =

acceleration)

T

:. F

α ma

α ma

F =kma (k = I ie unit constant)

Thus, the above implies that

**F = ma**

Hence, by definition, the

force that caused the motion of an object is defined as the product of the

mass of the body and its acceleration.

force that caused the motion of an object is defined as the product of the

mass of the body and its acceleration.

**Impulse and the momentum conservation principle**

The impulse is a force that acts over a little

period of time ie

period of time ie

I = Ft

I is the impulse, t is the

time and f is the force. Using the

second law of uniform motion ie

time and f is the force. Using the

second law of uniform motion ie

F

=

=

__ê____p__ T

Which implies that

Ft

=

=

__ê____p__ The above consequently

implies that the impulse I also defined as the change in momentum (

implies that the impulse I also defined as the change in momentum (

__ê____p)__of a of a body. Recall that êp = p2 – p1

Which implies that

êp = mv

– mu

– mu

êp = m(v-u)

êp = mêv

Again, the above implies that

impulse also define as the product of the mass of a body and its change in

velocity. The unit of impulse is Ns

(Newton second)

impulse also define as the product of the mass of a body and its change in

velocity. The unit of impulse is Ns

(Newton second)

**Note that**

Ft = êp

Ft = p2-

p1

p1

The above implies that

momentum can be conserved. For this to

be realistic, the force f should be zero

(O). This implies the momentum

conservation principle which states as follows:

momentum can be conserved. For this to

be realistic, the force f should be zero

(O). This implies the momentum

conservation principle which states as follows:

If the total force acting on a system is

zero, then the vector sum of the momentum is constant. Momentum is conserved in the following

systems

zero, then the vector sum of the momentum is constant. Momentum is conserved in the following

systems

(i)

During collision

During collision

(ii)

During explosion

During explosion

**Collision**

Collision is one of the system in which momentum is

constant. This simply implies that the

sum of momentum before collision is the same as the sum of momentum after

collision.

constant. This simply implies that the

sum of momentum before collision is the same as the sum of momentum after

collision.

Collision can however be

elastic, if not, it is inelastic. For

elastic collision, apart from momentum being conserved kinetic energy is also

conserved. For illustration, the

following diagram illustrate two bodies which are in collision.

elastic, if not, it is inelastic. For

elastic collision, apart from momentum being conserved kinetic energy is also

conserved. For illustration, the

following diagram illustrate two bodies which are in collision.

m1u1 m2u2

Before collision

m1v1 m2v2

After collision

Then for conservation of momentum we write:

m1u1

+ m2u2 m1v1 + m2v2 ……………………….

(i)

+ m2u2 m1v1 + m2v2 ……………………….

(i)

and for that of kinetic energy we

also write

also write

½ m1u1

+ m2u2 m1v1 + m2v2 ……………………..(ii)

+ m2u2 m1v1 + m2v2 ……………………..(ii)

Note that (i) and (ii) are

simultaneously obtained only if the collision is elastic.

simultaneously obtained only if the collision is elastic.

Example of elastic collision is the collision among the molecules of

ideal gases.

ideal gases.

Collision is inelastic if kinetic energy is not conserved. For instance,

a hall dropped into a muddy ground, its collision is not elastic ie inelastic

a hall dropped into a muddy ground, its collision is not elastic ie inelastic

**Explosion**

Apart from collision (elastic and inelastic), momentum is also conserved

during explosion. For instance, when a

bullet is being fire from a gun. During

explosion, though momentum is conserved but just like in inelastic collision,

kinetic energy is not conserved.

during explosion. For instance, when a

bullet is being fire from a gun. During

explosion, though momentum is conserved but just like in inelastic collision,

kinetic energy is not conserved.

Kinetic energy is used in differentiating between inelastic collision and

explosion, though in the two, kinetic energy is not conserved. During collision, the sum of the kinetic energy

after collision is less than sum of its kinetic energy before collision while

sum of the kinetic energy before explosion, is less than the sum of kinetic

energy after collision.

explosion, though in the two, kinetic energy is not conserved. During collision, the sum of the kinetic energy

after collision is less than sum of its kinetic energy before collision while

sum of the kinetic energy before explosion, is less than the sum of kinetic

energy after collision.

Example

A force of 15N is used to push a door for 5 seconds. What is the impulse of the door?

Solution

t – ?

p = 15N

t = 5s

I

= F x t

= F x t

t

= 15 x 5

= 15 x 5

= 75N secs

Example

Calculate the momentum of a

body of mass 4 kg moving with a velocity 50ms-1

body of mass 4 kg moving with a velocity 50ms-1

m = 4kg

v = 50ms

p = m x v

= 4 x 50

– 200kgm-1

– 200kgm-1

Example

When taking a penalty kick, a

footballer applies a force of 30,0N for a period of 0,05s. I f the mass of the ball is 0.075kg,

calculate the speed with which the ball moves off.

footballer applies a force of 30,0N for a period of 0,05s. I f the mass of the ball is 0.075kg,

calculate the speed with which the ball moves off.

Solution

f = 30N

t = 0.05s

u = 0

v = 0.075kg

m

= 0.075kg

= 0.075kg

From Newton’s

second law of motion

second law of motion

Ft = m(v-u)

30

x 0.05 = 0.075(v – 0)

x 0.05 = 0.075(v – 0)

V =

=20m/s

__30 x 0,05__=20m/s

0.075

Example

A 1kg cement is pushed along

brick of a building by a force of 50N A

fictional force of 15N opposes the motion.

Calculate the acceleration given to the cement.

brick of a building by a force of 50N A

fictional force of 15N opposes the motion.

Calculate the acceleration given to the cement.

Solution

Force F

= 50N – 15N

= 35N

= 50N – 15N

= 35N

Since F

= ma

= ma

35 =

I x a

I x a

A

=

35 ms-1

=

__35__=35 ms-1

**Application of Newton’s and conservation of Momentum**

Laws

Laws

**1.**

**Recoil of a Gun**

Before a

gun is fired, the initial momentum of the gun and bullet is equal to zero. When

the gun is fired, the bullet moves forward with a certain velocity say vr.Therefore

its momentum is equal to m1v1, where m2 is the

mass of the bullet. Suppose the mass of

the gum is m and also moving with velocity v2, from the law of

conservation of linear momentum.

gun is fired, the initial momentum of the gun and bullet is equal to zero. When

the gun is fired, the bullet moves forward with a certain velocity say vr.Therefore

its momentum is equal to m1v1, where m2 is the

mass of the bullet. Suppose the mass of

the gum is m and also moving with velocity v2, from the law of

conservation of linear momentum.

m1v1 + m2v2

m1v1 = m2v2

Which

shows that their moment is in opposite direction ie the momentum is on opposite

direction ie the momentum of the gun opposes that of the bullet. This is why the gun jerks backward or

recoils. It should also be noted that

the mass of the gun is heavier than that of the bullet ie (m1>>m2)

which then makes both the kinetic energy and the velocity of the bullet higher,

Then that of the gun.

shows that their moment is in opposite direction ie the momentum is on opposite

direction ie the momentum of the gun opposes that of the bullet. This is why the gun jerks backward or

recoils. It should also be noted that

the mass of the gun is heavier than that of the bullet ie (m1>>m2)

which then makes both the kinetic energy and the velocity of the bullet higher,

Then that of the gun.

2.

**Jet and Rocket Propulsion** Engines that are in Jet and rockets has a

combustion chamber in which the fuels (jet fuel in the case of jets) are

converted into gases to be burnt to provide the energy needed by the jets of

flight. As those gases are expelled

downward at very high speeds from the aircraft, an equal but opposite momentum is

given to the aircraft to enable them to fly.

combustion chamber in which the fuels (jet fuel in the case of jets) are

converted into gases to be burnt to provide the energy needed by the jets of

flight. As those gases are expelled

downward at very high speeds from the aircraft, an equal but opposite momentum is

given to the aircraft to enable them to fly.

**Summary**

1.

Momentum (p) of a body is defined as the

product of its mass and its velocity (p=mv).

Momentum (p) of a body is defined as the

product of its mass and its velocity (p=mv).

2.

Impulse is the product of the force and the

time during which the force acts (I = ft)

Impulse is the product of the force and the

time during which the force acts (I = ft)

3.

Newton’s first law of motion states that a

body will continue to be in a state of rest or of uniform motion in a straight

line unless acted upon by an external force,

It is also called the law of inertia.

Newton’s first law of motion states that a

body will continue to be in a state of rest or of uniform motion in a straight

line unless acted upon by an external force,

It is also called the law of inertia.

Newton’s second law of motion states

that the rate of change of momentum is proportioned to the force and takes

place in the direction of the force.

that the rate of change of momentum is proportioned to the force and takes

place in the direction of the force.

Newton’s third law states that action

and reaction are equal and opposite.

and reaction are equal and opposite.

4.

Principle

of conservation of linear momentum stares that in a system of colluding

objects, the total momentum is always conserved provided there is not external

force acting on the system.

Principle

of conservation of linear momentum stares that in a system of colluding

objects, the total momentum is always conserved provided there is not external

force acting on the system.

5.

There are two types of collision

There are two types of collision

(i)

Elastic

collision

Elastic

collision

(ii)

Inelastic collision

Inelastic collision

6.

Newton

law can be seen in

Newton

law can be seen in

(i)

Recoil

of gun

Recoil

of gun

(ii)

Jet and rocket propulsion

Jet and rocket propulsion

(iii)

Why walking is possible

Why walking is possible

7.

Mass is the quantity of matter in a body. The

unit of mass in kg and that fo weight is the Newton (N)

Mass is the quantity of matter in a body. The

unit of mass in kg and that fo weight is the Newton (N)

**References**

1.https://en.wikipedia.org/wiki/Isaac_Newton

2.Sciencedirect: fundamental concept of aerodynamics

3. New school physics by John Nelson (Revised 2015)