Consider the following statements : If the net external torque acting on an object is switched off, then 1. linear momentum will remain unchanged. 2. angular momentum wall remain unchanged. Which of the statements given above is/are correct?

1. Newton’s Laws and Linear Momentum (basic)

To master mechanics, we must first understand how things move in a straight line, which we call linear motion (Science-Class VII, Measurement of Time and Motion, p.116). Imagine a train moving along a straight track. If it maintains the same speed, it is in uniform linear motion; if it speeds up or slows down, its motion is non-uniform (Science-Class VII, Measurement of Time and Motion, p.117). The 'driver' behind these changes is Force, measured in Newtons (N) (Science, Class VIII, Exploring Forces, p.65). Newton’s laws tell us that an object’s state of motion only changes when a net external force is applied.

This brings us to a fundamental concept: Linear Momentum (p). Think of momentum as the 'quantity of motion' an object possesses. It is the product of an object's mass (m) and its velocity (v), expressed as p = mv. Newton’s Second Law defines force as the rate at which this momentum changes over time (F = Δp/Δt). If you apply a force to a moving ball, its velocity changes, and thus its momentum changes. Conversely, if no external force acts on the ball, its momentum stays exactly the same.

The Law of Conservation of Linear Momentum states that the total linear momentum of a system remains constant if the net external force acting on it is zero. This is a crucial distinction in physics: linear momentum is tied strictly to force. Even if an object is spinning or experiencing 'torque' (turning force), its linear momentum will only change if a net external force pushes or pulls it in a specific direction.

Concept	Definition	Dependency
Linear Momentum (p)	Mass × Velocity (mv)	Changed by Net External Force
Force (F)	Push or pull in Newtons (N)	Causes change in Linear Momentum

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117; Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.65

2. Forces and Translational Motion (basic)

At its simplest level, force is any interaction that, when unopposed, will change the motion of an object. In the context of translational motion—where an object moves as a whole from one point to another—force is the fundamental 'driver.' We categorize these interactions into contact forces, which require physical touch (like pushing a box), and non-contact forces, which act over a distance (like gravitational force) Science, Class VIII, NCERT, Exploring Forces, p.66. For a UPSC aspirant, the most crucial distinction to master is between internal and external forces.

Newton’s Second Law (F = ma) tells us that the net external force acting on an object determines its acceleration and, by extension, its change in linear momentum (p = mv). If a system is isolated and the net external force is zero, the linear momentum of that system remains constant (conserved). This is a pillar of classical mechanics: internal forces (like atoms pushing against each other inside a solid block) cannot change the total momentum of the block as a whole; only an external 'shove' can do that.

We see this principle applied even in the physical sciences of Earth. For instance, the Earth’s surface is constantly reshaped by exogenic forces (external forces like wind or water) and endogenic forces (internal forces like plate movements) FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT), Geomorphic Processes, p.37. In translational motion, we focus on the net result: if the forces acting in opposite directions are equal (like two air masses pushing against each other in a stationary front), there is no net motion in those directions Physical Geography by PMF IAS, Temperate Cyclones, p.399. Understanding that translational change requires a non-zero net external force is the first step toward mastering more complex rotational dynamics.

Sources: Science, Class VIII, NCERT, Exploring Forces, p.66; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT), Geomorphic Processes, p.37; Physical Geography by PMF IAS, Temperate Cyclones, p.399

3. Work, Energy, and Power (intermediate)

To understand mechanics, we must distinguish between the capacity to do work (Energy), the action of transferring energy (Work), and the rate of that transfer (Power). At its simplest, work is done when a force causes displacement. Interestingly, work isn't just about pushing boxes; in electrical systems, work is done by moving a charge (Q) across a potential difference (V), expressed as W = VQ Science, class X (NCERT 2025 ed.), Electricity, p.173. Energy, the fuel for this work, exists in many forms—from the chemical energy in our food to the sunlight captured by plants Science, class X (NCERT 2025 ed.), Our Environment, p.210. Power is simply how fast this energy is being used; for instance, the power input to a circuit is given by P = VI Science, class X (NCERT 2025 ed.), Electricity, p.188. Moving into intermediate mechanics, we must look at how these concepts govern motion through Conservation Laws. While energy is conserved in a closed system, Momentum follows specific rules based on the type of influence applied. There is a vital distinction between Linear Momentum (governed by Force) and Angular Momentum (governed by Torque). According to the law of conservation of angular momentum, the angular momentum (L) of a system remains constant if the net external torque (τ) acting on it is zero. This is mathematically written as dL/dt = τ; if τ = 0, then dL/dt = 0, meaning L is constant. Crucially, the conservation of one does not guarantee the conservation of the other. Torque is the rotational equivalent of force, defined as τ = r × F. It is entirely possible for a system to have a net external force (changing its linear momentum) while having zero net torque (preserving its angular momentum). For example, if you push an object exactly through its center of mass, you provide a force that moves it forward, but because the distance from the pivot (r) is zero, you exert no torque. Thus, its angular momentum remains conserved even though its linear momentum is changing.

Concept	Governing Influence	Conservation Condition
Linear Momentum	Net External Force (F)	F = 0
Angular Momentum	Net External Torque (τ)	τ = 0

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.173, 188; Science, class X (NCERT 2025 ed.), Our Environment, p.210

4. Circular Motion and Kepler’s Laws (intermediate)

To understand how planets move or why cyclones swirl, we must first distinguish between linear and angular motion. While linear motion is governed by forces, circular motion is governed by Torque (τ) and Angular Momentum (L). In any rotating system, like air flowing around a low-pressure center, a centripetal force acts toward the center of rotation to maintain the circular pattern Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309. However, the most profound insight into orbital mechanics comes from Kepler’s Second Law, which states that a planet sweeps out equal areas in equal intervals of time Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257. This means that as Earth moves closer to the Sun (at perigee), it must travel faster to cover the same area compared to when it is farther away (at apogee).

This orbital speed change is not random; it is a direct consequence of the Law of Conservation of Angular Momentum. Angular momentum (L) remains constant (conserved) as long as the net external torque acting on the system is zero (dL/dt = 0 when τ = 0). In a planetary system, gravity acts along the line connecting the planet and the sun, meaning the 'lever arm' for torque is zero, so no external torque is applied. This conservation explains why our northern hemisphere summers are slightly longer than winters—since Earth is farther from the sun in summer, its orbital velocity drops, taking more time to travel that segment of its orbit Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256.

It is vital to distinguish between the conservation of linear and angular momentum. While they seem similar, they depend on different physical conditions:

Concept	Conserved Property	Required Condition
Linear Momentum	P = mv	Net external Force (F) = 0
Angular Momentum	L = r × p	Net external Torque (τ) = 0

Crucially, a system can have a net external force acting on it (changing its linear momentum) while still having zero net torque (conserving its angular momentum). For instance, a force pulling a planet directly toward the Sun changes the planet's direction and linear velocity, but because it produces no torque, the planet's angular momentum remains perfectly conserved.

Sources: Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256

5. Understanding Torque (Moment of Force) (intermediate)

In our study of mechanics, we have seen that a Force is required to change the state of motion of an object Science, Class VIII NCERT, Exploring Forces, p.66. However, when we want to make an object rotate, it is not just the magnitude of the force that matters, but also where and how that force is applied. This "turning effect" of a force is what we call Torque (or Moment of Force).

Think of opening a heavy door. If you push near the hinges (the axis of rotation), it is incredibly difficult. If you push at the handle, far from the hinges, it opens easily. This is because Torque (τ) depends on three factors: the magnitude of the Force (F), the distance from the pivot point called the Lever Arm (r), and the angle between them. Mathematically, it is expressed as τ = r × F sin(θ). While the SI unit of force is the Newton (N) Science, Class VIII NCERT, Exploring Forces, p.65, the unit for torque is the Newton-meter (Nm).

A critical distinction to understand for the UPSC is the relationship between Torque and Angular Momentum (L). Just as Newton’s Second Law states that force is the rate of change of linear momentum (F = dp/dt), Torque is the rate of change of angular momentum (τ = dL/dt). If the net external torque acting on a system is zero, its angular momentum remains constant or "conserved." This is why some machines, like vertical-axis wind turbines, are designed to yield high torque even at slow speeds—to effectively manage the rotational energy of the system Environment, Shankar IAS Academy, Renewable Energy, p.290.

Feature	Linear Motion	Rotational Motion
Cause of Motion	Force (F)	Torque (τ)
Momentum Type	Linear Momentum (P)	Angular Momentum (L)
Governing Law	F = dp/dt	τ = dL/dt

Sources: Science, Class VIII NCERT, Exploring Forces, p.65; Science, Class VIII NCERT, Exploring Forces, p.66; Environment, Shankar IAS Academy, Renewable Energy, p.290

6. Conservation of Angular Momentum (exam-level)

In our journey through mechanics, we’ve seen how forces change linear motion. Now, let’s look at the rotational equivalent: the Law of Conservation of Angular Momentum. At its heart, this principle states that the total angular momentum (L) of a system remains constant if no net external torque (τ) acts upon it. In mathematical terms, torque is the rate of change of angular momentum (τ = dL/dt). If the net torque is zero, then dL/dt = 0, which means the angular momentum (L) is conserved (stays the same over time).

It is crucial to distinguish this from linear momentum. While the conservation of linear momentum depends on the net external force being zero, the conservation of angular momentum depends strictly on the net external torque. These are related but distinct: torque is a product of force and its distance from the axis of rotation (τ = r × F). A fascinating real-world example of this distribution is found in our solar system. While the Sun holds approximately 99.8% of the total mass, it accounts for only about 2% of the total angular momentum Physical Geography by PMF IAS, The Solar System, p.23. This shows how mass distribution and rotational velocity interact to define a system's angular momentum.

A common point of confusion in competitive exams is the relationship between force and torque. A zero net torque does not necessarily imply a zero net force. For instance, if you push a sliding block exactly through its center of mass, you apply a force that changes its linear momentum, but since the distance from the pivot (r) is zero, you exert zero torque. Thus, its angular momentum remains conserved (at zero) even though its linear momentum is changing. Conversely, in complex systems like a proton moving in a magnetic field, properties like velocity and momentum can change due to the forces exerted by the field, even if the mass remains constant Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.203.

Concept	Conserved If...	Governing Equation
Linear Momentum (p)	Net External Force (F) = 0	F = dp/dt
Angular Momentum (L)	Net External Torque (τ) = 0	τ = dL/dt

Sources: Physical Geography by PMF IAS, The Solar System, p.23; Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.203

7. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental definitions of force and torque, this question tests your ability to distinguish between translational and rotational equilibrium. You’ve learned that linear momentum is governed by Newton’s Second Law ($F = dp/dt$), while angular momentum follows its rotational analogue ($τ = dL/dt$). This question is a classic application of the Law of Conservation of Angular Momentum, which you just studied in the context of rigid body dynamics in NCERT Class 11 Physics.

To arrive at the correct answer, follow the mathematical logic: the question specifies that the net external torque is switched off ($τ = 0$). According to the relationship τ = dL/dt, if the torque is zero, the rate of change of angular momentum is zero, which means the angular momentum remains constant. Therefore, Statement 2 is correct. However, for linear momentum to remain unchanged, the net external force must be zero. Since a force can be applied directly through the axis of rotation or center of mass—thereby changing linear momentum while generating zero torque—we cannot conclude that statement 1 is true. Consequently, the correct option is (B) 2 only.

The UPSC often sets "symmetry traps" to catch students who assume that rotational and translational states always mirror each other. Many aspirants incorrectly choose (C) Both 1 and 2 because they reflexively associate a lack of "turning effect" with a total lack of "pushing force." As explained in Concepts of Physics by H.C. Verma, torque is a cross product of position and force; thus, you can have a non-zero force resulting in zero torque if the lever arm is zero. Always remember: torque only controls rotation, not the overall translational movement of the object.