Revision: Laws of Motion Physics (English Medium) ICSE Class 9 CISCE

The weight of the body is the force with which the earth attracts it towards the centre. It depends on acceleration due to gravity.

The gravitational force acting on an object is called the weight of the object.

A force is seen to act through direct contact of the objects or via one more object. Such a force is called 'Contact force.'

OR

The forces experienced by a body due to physical contact with another object, e.g., frictional force, normal force, are called contact forces.

A force is applied between two objects even if the two objects are not in contact; such a force is called a 'Non-contact force.'

OR

The forces experienced by a body without any physical contact with another object, e.g., gravitational force, electrostatic force, are called non-contact forces.

Inertia: The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force, is known as ‘inertia’.
Types of Inertia

• Inertia of rest
• Inertia of motion
• Inertia of direction

Newton’s second law of motion states that the rate of change of momentum is directly proportional to force applied and takes place in the direction of the force.

The gravitational force due to the earth on a body results in its acceleration. This is called acceleration due to gravity and is denoted by ‘g’.

OR

When a body falls towards the Earth under gravity, then the acceleration produced in the body due to gravity is called acceleration due to gravity, which is denoted by g.

The acceleration produced in a body under the influence of the force of gravity alone is called acceleration due to gravity.

The weight of an object is defined as the force with which the earth attracts the object.

Mass is the amount of matter present in the object. The SI unit of mass is kg.

Absolute unit of force in the CGS system is dyne and in SI system is Newton (N).
One dyne: When the body of mass 1 gram moves with an acceleration of 1 cms⁻², then the force acting on the body is called one dyne.
1 dyne = 1 g cms⁻²
One Newton: When a body of mass 1 kg moves with an acceleration of 1 ms⁻², then force acting on the body is said to be one newton.

OR

That force is said to be one newton, which producers an acceleration of 1 ms⁻² in a body of mass 1 kg.
1 N = 1 kg ms⁻²

"Every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

\[\vec F\] = m \[\frac{d\vec{\mathrm{v}}}{dt}\] = m\[\vec a\] ... (for constant mass)

Thus, if \[\vec F\] = 0, \[\vec v\] is constant. Hence, if there is no force, velocity will not change. This is nothing but Newton's first law of motion.

General Form: \[\vec F\] =\[\frac{d\vec{p}}{dt}\]

For Constant Mass: \[\vec F\] = m\[\vec a\]

Momentum: \[\vec p\] = m\[\vec v\]

\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]

The value of the acceleration due to gravity (g) on the surface of the Earth is given by the formula:

Where:

• g = Acceleration due to gravity (in m/s²).
• G = Newton's Universal Gravitational Constant (≈ 6.67 × 10⁻¹¹ N · m² / kg²).
• M = Mass of the Earth (≈ 6 × 10²⁴ kg).
• R = Radius of the Earth (≈ 6.4 × 10⁶ m).

The gravitational force of attraction (F) between two bodies of mass m₁ and m₂ separated by a distance r is:

• F: Gravitational Force of attraction (in Newtons, N).

• \[m_1, m_2\]: Masses of the two objects (in kilograms, kg).

• r (or d in the first part): Distance between the two objects (in meters, m).

• G: The constant of proportionality, called the Universal gravitational constant.

  • Value in SI units: \[G=6.67\times10^{-11}\mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2\]

  • Dimensions: \[[G]=[\mathrm{L}^3\mathrm{M}^{-1}\mathrm{T}^{-2}]\]

Statement:

Every inanimate object continues to be in a state of rest or of uniform unaccelerated motion along a straight line, unless it is acted upon by an external, unbalanced force.

Importance:

• It shows the equivalence between the state of rest and the state of uniform motion along a straight line — the distinction lies only in the choice of frame of reference.
• It defines force as a physical entity that brings about a change in the state of motion or rest of an object.
• It defines inertia as a fundamental and inherent property of every physical body by virtue of which it resists any change in its state of rest or uniform motion along a straight line.

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.

F = Δp = m\[\frac {dv}{dt}\] = ma

Importance:

• It provides a mathematical formulation for the quantitative measure of force: F = \[\frac {Δp}{Δt}\] = ma.
• It defines momentum as the product of mass and velocity: p = mv.
• Aristotle's fallacy is overcome by establishing that it is the resultant unbalanced force — not force itself — that is required to maintain a change in the state of motion.

Statement:

To every action (force) there is always an equal and opposite reaction (force).

Importance:

• It defines action and reaction as a pair of equal and opposite forces acting along the same line — whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first.
• Action and reaction forces always act on different objects and therefore never cancel each other out.

Statement:

The law which states that every particle of matter attracts every other particle in the universe with a force whose magnitude is directly proportional to the product of masses and inversely proportional to the square of distance between them is called Newton's Law of Gravitation.

Derivation:

Newton's Universal Law of Gravitation states that every particle of matter attracts every other particle of matter with a force which is:

• Directly proportional to the product of their masses: F ∝ m₁ ⋅ m₂
• Inversely proportional to the square of the distance between them: F ∝ \[\frac {1}{r^2}\]

Combining both, the gravitational force is expressed as:

F = G\[\frac{m_1m_2}{r^2}\]

where G is the Universal Gravitational Constant, measured by Henry Cavendish using the Cavendish balance, with the value:

G = 6.67 × 10⁻¹¹Nm²/kg²

• Due to Altitude: The acceleration due to gravity decreases with altitude as we move away from the surface of the Earth. As h↑, g↓.
• Due to Depth: The acceleration due to gravity decreases as we move into the Earth's interior, i.e., with increasing depth. As d↑, g↓.
• Due to Latitude: The acceleration due to gravity increases with latitude. At the poles (θ = 90°), g = g_max⁡​; at the equator (θ = 0°), g = g_min​.
• Due to Shape of Earth: The equatorial radius of the Earth is greater than the polar radius. Since g ∝ \[\frac {1}{R^2}\], the acceleration due to gravity is greater at the poles compared to the equator, i.e., R_equator > R_pole​ and g_equator < g_pole​.