Revision: Laws of Motion >> Laws of Motion Physics Science (English Medium) Class 11 CBSE

Aristotle's statement: “An external force is required to keep a body in uniform motion”.

The inability of a body to change its state of uniform motion by itself is called inertia of motion.

The inability of a body to change its direction of motion by itself is called inertia of direction.

The inability of a body to change its state of rest or of uniform motion or its direction by itself is called Inertia.

The inability of a body to change its state of rest by itself is called inertia of rest.

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 force acting on a particle performing uniform circular motion along the radius and directed towards the centre of the circle is called the centripetal force.

The mathematical form of centripetal force is:

F = `mv^2/r`

where:

F = centripetal force,

m = mass of the object,

v = speed or velocity, and

r = radius

When a particle moves in two dimensions or in a plane such that its distance from a fixed (or moving) point remains constant, then its motion is called circular motion.

The circular motion in which the speed of a particle is constant but its direction changes continuously, and acceleration is always directed towards the centre, is called uniform circular motion.

The force directed along the radius towards the centre of a circle, which is necessary to keep the object moving in a circle, is called centripetal force.

The non-real (fictitious) force directed along the radius away from the centre of a circle (opposite to centripetal acceleration) is called centrifugal 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.

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 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.

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

"Friction between two bodies in contact when one body is rolling over the other, is called rolling friction."

OR

The resistive force or rolling resistance that occurs when an object rolls across a surface and slows down the motion of a rolling ball/wheel, which is the weakest form of friction compared to static/sliding friction, is called Rolling Friction.

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

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

\[\vec{F}=-\frac{mv^2}{r}\hat{r}_0\]

Directed towards the centre (negative sign indicates inward direction).

\[\vec{F}=+\frac{mv^2}{r}\hat{r}_0\]

Directed away from the centre (positive sign indicates outward direction).

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

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.

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

Statement: The law of inertia shows that a body will preserve its velocity and direction till no force in the direction of its motion acts upon it.

• A more massive object has more inertia.
• To maintain uniform motion along a straight line, balanced forces are required.
• Unbalanced external forces acting on a body can only bring a change in its state of motion.

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 total momentum of a system of particles remains constant as long as no external forces act upon it.

• When no external forces act on colliding objects, the vector sum of linear momentum of each body remains constant and is not affected by mutual interaction.

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).

Statement: The initial momentum of a rocket at its launching pad is zero. When fired, the exhaust gases rush downward at high speed. To conserve momentum, the rocket moves upwards.

Thrust on the rocket:

The negative sign indicates that the direction of thrust is opposite to the direction of escaping gases.

Acceleration of the rocket:

where v = velocity of exhaust gases and \[\frac {dm}{dt}\]​ = rate of fuel consumption = rate of ejection of fuel.