Revision: Laws of Motion Science SSLC (English Medium) Class 10 Tamil Nadu Board of Secondary Education

1 dyne is that force which when acting on a body of mass 1 gram, produces an acceleration of 1 cm s^-2 in it.
1 dyne = 1 g × 1 cm s^-2.

The forces which are applied on a body through a connector, are called contact forces. Forces like Frictional force, Mechanical force, etc., are the forces of contact.

An inclined plane is usually a smooth, flat rigid surface inclined at an angle (θ) to the horizontal. It is used to raise heavy loads with a relatively small force. The longer the slope, the smaller is the effort needed.

Force is defined as the rate of change of linear momentum of a body with respect to time.

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

When a force acts on a stationary rigid body that is free to move, the body starts moving in a straight path in the direction of the applied force. This is called linear or translational motion.

Now consider a body pivoted at a point, i.e., not free to move, and a force is applied on the body at a suitable point, it rotates the body about the axis passing through the pivoted point. This is the turning effect of the force and the motion of the body is called rotational motion.

The physical quantity is ‘torque’.

Torque may be defined as the turning effect produced by a force on a rigid body about a point, pivot, or fulcrum. It is measured by the product of force and the perpendicular distance of the pivot from the line of action of force.

Force is a physical cause that changes or may tend to change the state of rest or the state of motion of an object. 

The turning effect produced by a force on a rigid body about a point, pivot or fulcrum is called the moment of force or torque. It is measured by the product of force and the perpendicular distance of the pivot from the line of action of force.

Moment of a force = Force × perpendicular distance of the pivot from the force.

The turning effect of force acting on a body about an axis is called the moment of force.

The moment of a force (or torque) is equal to the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation. 

The forces which act on a body without the help of any connector, are called non-contact forces or forces of distance. Gravitational force, Mechanical force, etc., are non-contact forces.

The perpendicular distance between the two forces is AB ( = d), which is called the couple arm.

Two equal and opposite parallel forces, not acting along the same line, form a couple. A couple is always needed to produce a rotation.

The moment of a couple is equal to the product of either force and the perpendicular distance between the line of action of both the forces.

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 quantity ‘change in momentum’ is separately named as the Impulse of the force.

OR

The quantity change in momentum is called impulse.

OR

Impulse
The product of a large force applied on a body for a very short interval of time, which produces a finite change in the momentum of the body, with SI unit Ns (or kg-ms⁻¹) and dimension [MLT⁻¹], is called impulse.

"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."

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 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.

\[\overset{\rightarrow}{\operatorname*{F}}=\frac{d\overset{\rightarrow}{\operatorname*{p}}}{dt}=\frac{d(m\overset{\rightarrow}{\operatorname*{v}})}{dt}\]

or

\[\begin{array}
{rcl}\vec{F} & = & m\vec{a}
\end{array}\](if mass m is constant)

\[\vec F\] = 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.

Moment of force = Force × perpendicular distance from the point (axis) of rotation

τ =  F × d

Moment of Couple = Either force x perpendicular distance between the two forces (or couple arm) 

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

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

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

\[{\vec{\mathrm{J}}=\vec{\mathrm{F}}t}=\mathrm{m}(\vec{\mathrm{v}}-\vec{\mathrm{u}})\]

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

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

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).

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: The impulse of a force equals the change in momentum of the body.

• When a force acts from time t₁ to t₂​:

• Impulse from a force-time graph = Area under the F-t graph.
• For constant force: J = Ft

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

• Force is a Vector Quantity
• Unit of Force is Newton (symbol N) or kilogram-force (symbol kgf), where 1 kgf = g N if g is the acceleration due to gravity at that place (= 9·8 m s^-2 average value on the earth's surface). 

• A force applied to a pivoted body causes rotation (not linear motion) about the axis passing through the pivot point.
• The turning effect of a force (torque) depends on two factors:
  The magnitude of the force
  The perpendicular distance from the axis of rotation
• Maximum torque is produced when the force is applied at the maximum perpendicular distance from the axis.
• The S.I. unit of moment of force is newton-metre (N·m), and the C.G.S. unit is dyne-centimetre.
• Anticlockwise moments are taken as positive and directed outwards from the axis, while clockwise moments are negative and directed inwards.

• 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​.