# Laws of motion

Inertia of rest and motion:

Inertia of rest:

It is the inability of body to change by itself, its state of rest. It is the inability of body to change, its state of rest by itself. This means that body at rest will remain at rest and cannot start moving on its own. This means a body at rest will remain at rest and cannot start moving on its own.

Inertia of motion:

It is the inability of the body to changes it state of uniform motion, which cannot be accelerated or retard on its own and comes to rest.

Momentum:

Moving body tries to exert force on anything that tries to stop it. The faster the object is travelling the harder it is to stop. So, this quality of a moving body is called as momentum. It is a vector quantity so therefore it has direction. The S.I unit of momentum is kilograms per second  $\frac{{{\rm{kgm}}}}{{\rm{s}}}$

Momentum can also be expressed as Newton second Ns.

Angle of friction:

The angle of a plane to the horizontal, when the body placed on the plane will just start to slide. This phenomenon is called as angle of friction. For example consider a block placed on a rough. The reaction force acting on the block will be ${\rm{\vec R}}$, because it is equal and opposite to the weight ${\rm{\vec W}}$. Now by applying the force in horizontal direction ${\rm{\vec P}}$ the block will just begin to slide, under such situation friction force will be equal to the limiting force. When this condition is fulfilled, the resultant angle will be angle of friction.

Formula of angle of friction:

tan$\theta = \mu {\rm{s}}$

Angle of repose;

The maximum slope, measured in degrees from the horizontal. At which loose materials will remain in place without sliding. This is known as angle of repose. For example when the platform of truck containing the stones in raised to a certain angle so that the stones begin to slide down,This is because the gravitational force along the platform just overcomes the frictional force. This angle, to which the platform is inclined with the horizontal, will be the angle of repose.

Relationship between angle of friction and angle of repose:

Angle of repose is defined as a minimum angle of inclination of a plane structure with the horizontal such that a body kept on it just begins to slide down to the plane. Let us consider a mass m is kept on the plane surface AB and it is inclined to angle θ such that the object begins to slide.

The component of the weight mg normal to the surface is mg cosθ which is balanced by the reaction force R and the component mg sinθ acts along the inclined surface which is balanced by frictional force

mgsinθ = Fs………………………………i

mgcosθ = R…………………..ii

from above

$\frac{{{\rm{mgsin}}\theta }}{{{\rm{\:mgcos}}\theta {\rm{\: }}}}{\rm{\: }} = \frac{{{\rm{Fs}}}}{{\rm{R}}}$

Tanθ = $\frac{{{\rm{Fs}}}}{{\rm{R}}}$

As,μ  = $\frac{{{\rm{Fs}}}}{{\rm{R}}}$

Tanθ  = μ

This shows that tangent of angle of repose is equal to the coefficient of friction between the surfaces.

Momentum and impulse:

Momentum

The momentum of an object is defined as the product of its mass and velocity. It is a vector quantity so therefore it has direction. The S.I unit of momentum is kilograms per second$\frac{{{\rm{kgm}}}}{{\rm{s}}}.$ Momentum can also be expressed as Newton second Ns.

Impulse:

Change in the momentum of the body is called as Impulse. For example when a bat hits a cricket ball, the force certainly varies during this collision. In this case F × t will be called as force of the impulse.

Impulse=${\rm{F}} *{\rm{t}} = {\rm{mvf}} - {\rm{mvi}}$

Newton’s third law of motion:

Newton's third law states for every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on second object

1. When we sit in chair, our body exerts a downward force on the chair and the chair exerts an upward force on our body. There are two forces resulting from this interaction a force on the chair and a force on our body. These two forces are called action and reaction forces

2. Suppose a person slams the wall with his fist. The force applied by the person through his fist on the wall is equal to the force applied by the wall on the fist. Harder the person slams the wall, more he gets hurt. Similar procedure is followed when a person kicks the football.

3. Force exerted by the hammer on the nail is action and the force exerted by the nail on the hammer is reaction. Here the force exerted by the hammer on the nail is equal in magnitude and opposite in direction to the force applied by the nail on the hammer.

4. When rocket moves in the space it pushes the gas outside from it, i.e., rocket applies force on the gases in the backward direction. As a reaction, the gases put equal amount of force on the rocket in the opposite direction and the rocket moves in the forward direction.

5. Ball follows the projectile motion and accelerates towards the earth due to the force of gravity applied by the earth on the ball. In the similar way ball also applies same force to the earth and tries to attract the earth towards it. But the earth mass is very large, so the acceleration produced in the ball is very small or negligible.

Newton’s laws of motion:

First law of motion:

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

Second law of motion

It states that the rate of change of momentum of the body with respect to the time is directly proportional to external force applied and the changes take plac in the direction of force .

F ∝$\frac{{{\rm{dp}}}}{{{\rm{dt}}}}$

F = K$\frac{{{\rm{dp}}}}{{{\rm{dt}}}}$

Where k is proportionality constant whose value is chose to be 1

F = $\frac{{{\rm{d}}\left( {{\rm{mv}}} \right)}}{{{\rm{dt}}}}$  = F = $\frac{{{\rm{mdv}}}}{{{\rm{dt}}}}$

∴ F = ma

Newton’s third law of motion:

Newton's third law states for every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on second object

1. When we sit in chair, our body exerts a downward force on the chair and the chair exerts an upward force on our body. There are two forces resulting from this interaction a force on the chair and a force on our body. These two forces are called action and reaction forces

2. Suppose a person slams the wall with his fist. The force applied by the person through his fist on the wall is equal to the force applied by the wall on the fist. Harder the person slams the wall, more he gets hurt. Similar procedure is followed when a person kicks the football.

3. Force exerted by the hammer on the nail is action and the force exerted by the nail on the hammer is reaction. Here the force exerted by the hammer on the nail is equal in magnitude and opposite in direction to the force applied by the nail on the hammer.

4. When rocket moves in the space it pushes the gas outside from it, i.e., rocket applies force on the gases in the backward direction. As a reaction, the gases put equal amount of force on the rocket in the opposite direction and the rocket moves in the forward direction.

5. Ball follows the projectile motion and accelerates towards the earth due to the force of gravity applied by the earth on the ball. In the similar way ball also applies same force to the earth and tries to attract the earth towards it. But the earth mass is very large, so the acceleration produced in the ball is very small or negligible.

Principles of conservation of linear momentum:

The law of conservation of linear momentum states that if no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction. Whenever there is change is momentum of the given body there is change of the velocity hence acceleration .According to the Newton’s 1st law of motion, the change in motion is produced by the external force .so, change in momentum and force are interrelated. This shows that conservation of momentum follows the Newton’s laws.

Laws of solid friction:

The frictional force between two surfaces opposes their relative motion.

The frictional force depends upon the roughness of the surface.

The frictional forces ids parallel to the surface in contact

The frictional forces is independent of the area of contact of the two surfaces

The kinetic friction is independent of the relative velocities of the surfaces.

The magnitude of frictional force is directly proportional to the normal reaction.

When a bus suddenly stops, a passenger standing in it is thrown forward:

Newton’s first law states that: an object will stay at rest unless acted upon by an unbalanced force. This principle is known as inertia, the property of an object to stay at rest or continue in motion unless disturbed. When a bus suddenly stops, the brakes have created an unbalanced force that quickly stops the motion of the bus, but have not changed your inertia. The only method by which the bus can stop a person is through friction whether they are sitting in a seat or standing up. When the bus stops, your inertia has not been changed and you will continue in motion by moving forward.

In order to swim, a person pushes the water backward:

According to Newton’s third law for every action there is an equal and opposite reaction. Therefore, when the person pushes the water in the backward direction, the water pushes him forward, when the person applies force on water in the backward direction, then the water also applies force as a reaction in the forward direction.

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