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

"If no force is acting on a body, its velocity does not change, i.e., the body does not accelerate. In other words, if a body is stationary, it will remain stationary. If it is in motion, it will continue moving with the same velocity and in the same direction."

or

"An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it."

or

"Every inanimate object continues to be in its state of rest or of uniform unaccelerated motion unless and until it is acted upon by an external, unbalanced force."

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 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.

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 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 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.

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 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.

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 rate of change of momentum is proportional to the applied force, and the change of momentum occurs in the direction of the force."

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.

"Every action force has an equal and opposite reaction force which acts simultaneously."

The concise law statement is: "To every action (force), there is an equal and opposite reaction (force)."

"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’.

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\[\vec v\]

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

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).

• 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.