Revision: Laws of Motion Physics (Theory) ISC (Science) ISC Class 11 CISCE

The support force exerted perpendicularly by a surface on an object in contact with it is called the normal force.

The push or pull which, when applied on an object, changes or tends to change (i) the state of rest, (ii) the state of uniform motion, or (iii) the shape and size of the object, measured in newton with dimension [MLT⁻²], is called Force.

The force which acts through direct physical contact between two objects, such as Frictional Force, Tensional Force, Normal Force, Air Resistance Force, Applied Force, and Spring Force, is called Contact Force.

The force which can act over distances without any physical contact between objects, such as Gravitational Force, Electrical Force, and Magnetic Force, is called Long Range or Non-contact Force.

The force of gravity on Earth which is always equal to the weight of the body, expressed as F_grav = mg where g = 9.8 m/s², is called Gravity Force.

The force which is applied to an object by a person or another object is called applied Force.

The force transmitted by a string, rope, or wire when pulled tightly by forces acting from its ends, whose magnitude is the same everywhere in the rope, is called tension Force.

The force exerted by a compressed or stretched spring upon or by an object, expressed as F_spring = −kx (Hooke's Law), is called spring Force.

The vector sum of all forces acting on an object is called Net Force.

The force which is exerted by a surface on a moving object or on an object making an effort to move, expressed as F_f = μ × F_N where μ is the coefficient of friction, is called Friction 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.

Friction between two surfaces in contact when one body is actually sliding over the other body is called kinetic friction or dynamic friction.

OR

The force of friction that comes into play when a body is in a steady state of motion over another surface is called the force of kinetic friction.

OR

The resistive force that acts between moving surfaces that are in relative motion, always acting opposite to the direction of velocity and tending to slow down the speed of an object, expressed as F_k = μ_k × N, is called Kinetic Friction.

For two masses m₁ and m₂ connected by a string over a pulley:

1. Acceleration: a = \[\frac{(m_1-m_2)}{m_1+m_2}\] × g

2. Tension: T = \[\frac{2m_1m_2}{m_1+m_2}\] × g

\[\vec F\] = 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\[\vec v\]

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

μₖ = Fₖ/N

The coefficient of kinetic friction is defined as the ratio of force of kinetic friction to the normal reaction between the two surfaces in contact.

Fₖ = μₖ N

Where:

• Fₖ = Force of kinetic friction
• μₖ = Coefficient of kinetic friction (constant of proportionality)
• N = Normal reaction between the two surfaces in contact

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: When three forces F₁, F₂ and F₃ act on a body and are in equilibrium, each force is proportional to the sine of the angle between the other two forces.

Formula:

where α, β, and γ are the angles opposite to forces F₁, F₂, and F₃ respectively.

• Newton's First Law states that a body at rest or in uniform motion stays that way unless an external unbalanced force acts on it.
• The law explains inertia, which is an object's resistance to changing its state of motion on its own.
• The 'state of rest' and 'state of uniform motion' are considered equivalent; both require a net unbalanced force to change.
• Force is defined by the law as the entity that changes a body’s state of motion.
• A balanced force results in a net force of zero, meaning no acceleration.
• An unbalanced force results in a net force that causes acceleration and changes the state of motion.
• Inertia is quantitatively measured by the object's mass (inertial mass).