PHYSICS11 4.Laws Of Motion

PHYSICS11

Chapter No 4.Laws Of Motion

Newton's first law:

Statement

every inanimate object continuous to be in a state of rest or of uniform uniform motion along a straight line unless it is acted upon by an external unbalance force.

Newton second law:

statement

The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.

Newton's third law

statement

To every action there is always an equal and opposite reaction.
Inertial frame of reference
Inertial frame of reference is a frame of reference in which Newton's laws of motion are verified.

Non inertial frame of reference

A frame of reference in which Newton's laws of motion are not verified.

Kinematics

In Which motion describe without it's cause.

Dynamics
In Which motion describe along with its cause.

Contact force
The force experienced by a body due to Physical contact is called contact force.

Non contact force
The force which experience by a body without any physical contact is called non contact force.

Real force

A force which is produced due to actual interaction between the objects is called real force.

Pseudo force
Pseudo force is one which arises due to accelerated frame of reference.

Conservative force
if work done by a force or against a force is independent of the actual path. The force is said to be a conservative force.

Non conservative force
If work done by a force or against a force is dependent of the actual path. The force is said to be a non conservative force.

Centre of mass
A point at which the whole mass of body is supposed to be concentrated is called centre of mass of that body.

Centre of gravity
A point at which the whole weight of body is supposed to be concentrated called centre of gravity of that given body.

Fundamental forces
1)Gravitational force
2)Electromagnetic force
3) Nuclear force
i )Strong nuclear force
ii )Weak nuclear force

FUNDAMENTAL FORCES IN NATURE

1)Gravitational force

2)Electromagnetic force

3) Strong nuclear force

4) Weak Nuclear force

Gravitational force

1)Force of mutual attraction between two bodies due to their masses.

2)It is a universal force

3) It obeys inverse square law

4) Weakest force of all forces.

5)It is Independent of intervening medium.

6)It is a non-contact force
7) Long range force

Electromagnetic force

1)The force between charged particles.

2) May be repulsive or attractive

3)Depends on the intervening medium.

4)Electric force between two protons, Example, is 10³⁶times the gravitational force between them, for any fixed distance.

5)The forces like ‘friction’, ‘normal force’, ‘spring force’, ‘tension’,etc. are

electromagnetic.

6))Large compared to gravitational force
7)Acts over large distances.

Strong nuclear force

1) The strong nuclear force binds protons and neutrons in a nucleus.

2) Attractive in nature

3) Strongest force in nature-about 100 times the electromagnetic force in strength.

4) It is charge-independent and acts equally between a proton and a proton, a neutron and a neutron, and a proton and a neutron.

5) Short range force-about nuclear dimensions.

Weak nuclear force

1) Appears only in certain nuclear processes such as the β-decay of a nucleus.

2)In β-decay, the nucleus emits an electron and an uncharged particle called neutrino.

3) The electron and neutrino interacts through weak force. not as weak as the gravitational force, but

much weaker than the strong nuclear and electromagnetic forces.

4) The range of weak nuclear force is exceedingly small, of the order of 10^-16

Ratio of strengths of forces

Strong force > electromagnetic force> weak force > gravitational force

SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

RIGID BODY

1)A rigid body is a body with a perfectly definite and unchanging shape.

2) The distances between different pairs of such a body do not change.

MOTIONS OF A RIGID BODY

PURE TRANSLATION

In pure translational motion at any instant of time every particle of the body has the same

velocity.

TRANSLATION AND ROTATION

Points P1, P2, P3 and P4 have different velocities at any instant of time.

• The line along which the body is fixed is termed as its axis of rotation.

CENTRE OF MASS

Centre of mass is the point at which the entire mass of the body can be assumed to be

concentrated.

For two particle system as shown in fig. the centre of mass is given by

If the two particles have the same mass , then

If we have n particle

The centre of mass C of the system of the three particles is defined and located by the

coordinates (X, Y) given by

PROBLEM

Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of

the particles are 100g, 150g, and 200g respectively. Each side of the equilateral

triangle is 0.5m long.

Moment of force (Torque)

The rotational analogue of force is moment of force or torque.

Torque is given by

The moment of force (or torque) is a vector quantity.

The symbol τ stands for the Greek letter tau. The magnitude of τ is

Moment of force has dimensions same as those

of work or energy [M¹L²T^-2]

Moment of a force is a vector, while work is a scalar.

The SI unit of moment of force is Newton-metre (Nm).

Angular momentum of a particle

Angular momentum is the rotational analogue of linear momentum.

The angular momentum is given by

The magnitude of the angular momentum vector is

Relation Between Angular Momentum and Torque

Differentiating with respect to time,

Thus, the time rate of change of the angular momentum of a particle is equal to the torque acting on it.

For a system of n particles, the total angular momentum is

Conservation of Angular Momentum

If the external torque acting on a system is zero, then

Thus if total external torque on a system is zero the angular momentum is conserved.

EQUILIBRIUM OF A RIGID BODY

A rigid body is said to be in mechanical equilibrium, if both its linear momentum and

angular momentum are not changing with time.

Translational equilibrium

The vector sum of the forces, on the rigid body is zero - linear momentum is conserved.

Rotational equilibrium

The vector sum of the torques on the rigid body is zero - angular momentum is
conserved.

Partial equilibrium

When two parallel forces both equal in magnitude are applied perpendicular to alight rod , the system will be in rotational equilibrium, and not in translational equilibrium.

When two forces are applied perpendicular in two opposite directions, the body is in

translational equilibrium; but not in rotational equilibrium.

Couple

A pair of equal and opposite forces with different lines of action is known as a couple.
A couple produces rotation without translation.
When we open the lid of a bottle by turning it, our fingers are applying a couple to the lid.

Principle of moments

For a lever at equilibrium the moment on the left = moment on the right

load arm × load = effort arm × effort

This is the principle of moments.

Anticlockwise moments - positive

Clockwise moments - negative

Centre of gravity

The CG of a body is the point where the total gravitational torque on the body is zero.
If acceleration due to gravity is same at all parts of a body, its centre of gravity coincides with centre of mass.
If g varies centre of gravity and centre of mass are different.