Linear vs Rotational Comparison

8 MCQs4 revision cards9-step worked example

Source: NCERT System of Particles and Rotational MotionPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

Every linear-motion quantity has a rotational twin. NCERT Class 11 Physics Chapter 7 (System of Particles and Rotational Motion), page 15, presents the comparison table that maps displacement → angular displacement, velocity → angular velocity, acceleration → angular acceleration, mass → moment of inertia, force → torque, momentum → angular momentum, and kinetic energy → rotational kinetic energy. This mapping is what NEET tests when it asks you to "write the rotational analogue of" a linear equation.

The structural rule is: replace every linear variable with its angular counterpart, and the equation's form stays identical.

Linear	Symbol	Rotational	Symbol
Displacement	s	Angular displacement	θ
Velocity	v	Angular velocity	ω
Acceleration	a	Angular acceleration	α
Mass (inertia)	m	Moment of inertia	I
Force	F	Torque	τ
Momentum	p = mv	Angular momentum	L = Iω
Kinetic energy	½mv²	Rotational KE	½Iω²
Newton's 2nd law	F = ma	Rotational form	τ = Iα

Two points where students lose marks:

1. The analogue of mass is I, not m. Moment of inertia depends on both mass AND its distribution about the axis. Two objects of the same mass can have different I values. When a question says "write the rotational analogue of ½mv²," the answer is ½Iω² — substituting m with I and v with ω.

2. Units shift but dimensional structure is preserved. Torque is N·m (not just N), angular momentum is kg·m²/s (not kg·m/s). If you write the rotational analogue but keep linear units, NEET marks it wrong.

The comparison table is a recall item — NEET can and does test it as a straightforward "which quantity is the analogue of..." question.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The rotational analogue of linear momentum (p = mv) is:

MCQ 2Easy RecallPractice

Which of the following is the rotational analogue of force?

MCQ 3Easy RecallPractice

In the rotational analogue of Newton's second law, mass (m) is replaced by:

MCQ 4Direct ApplicationPractice

The rotational kinetic energy of a body rotating about a fixed axis is given by ½Iω². This expression is the rotational analogue of:

MCQ 5Direct ApplicationPractice

A disc of moment of inertia 4.0 kg·m² rotates at angular velocity 3.0 rad/s about a fixed axis. Its rotational kinetic energy is:

MCQ 6Direct ApplicationPractice

The SI unit of angular momentum is:

MCQ 7Concept TrapPractice

Two bodies A and B have the same mass and the same angular velocity about a fixed axis. If A has a larger moment of inertia than B, which statement is correct?

MCQ 8Easy RecallPractice

The linear equation v = u + at has the rotational analogue ω = ω₀ + αt. In this analogy, the quantity that replaces linear acceleration 'a' is:

Quick recall before you leave

Worked Example

1
Given
A uniform solid cylinder of mass M = 2.0 kg and radius R = 0.10 m rolls without slipping on a horizontal surface. Its centre of mass moves at v = 4.0 m/s.
2
Required
Find the ratio of rotational kinetic energy to translational kinetic energy.
3
Concept
For a rolling body, KE_total = KE_trans + KE_rot = ½Mv² + ½Iω². The linear–rotational analogy gives us the rotational KE term by replacing m with I and v with ω. For rolling without slipping, v = Rω, so ω = v/R.
4
Formula
KE_trans = ½Mv² KE_rot = ½Iω² For a solid cylinder about its symmetry axis: I = ½MR² Rolling constraint: ω = v/R
5
Substitution
KE_rot = ½ × (½MR²) × (v/R)² = ½ × ½MR² × v²/R² = ¼Mv² KE_trans = ½Mv²
6
Calculation
Ratio = KE_rot / KE_trans = (¼Mv²) / (½Mv²) = (¼)/(½) = 1/2 Note on exact constants: The coefficients ½ (in KE formulas and in the cylinder's MOI formula ½MR²) are exact mathematical/geometric constants. They do not limit significant figures. The given values M = 2.0 kg, R = 0.10 m, v = 4.0 m/s each have 2 significant figures, but since M, R, and v all cancel in the ratio, the answer is an exact fraction.
7
Final answer
KE_rot / KE_trans = **1/2** (or equivalently, rotational KE is one-half of translational KE for a rolling solid cylinder). This means one-third of the total KE is rotational and two-thirds is translational.
8
Common trap
A common error is using the wrong MOI coefficient — plugging in I = MR² (ring) instead of I = ½MR² (solid cylinder). With the ring formula, the ratio would come out as 1 instead of ½. Always verify the geometry before picking I.
9
Similar NEET-style question
A solid sphere of mass 3.0 kg rolls without slipping at 5.0 m/s. What fraction of its total kinetic energy is rotational? (Hint: I_sphere = 2MR²/5; use the same ratio method.) ---

Before solving, remember these

Key Fact

Linear–rotational analogy

Translation ↔ Rotation: F ↔ τ, m ↔ I, v ↔ ω, a ↔ α, p = mv ↔ L = Iω, KE = ½mv² ↔ KE_rot = ½ I ω². Newton's 2nd Law analogue: τ = I α.

-- NCERT Class 11 Physics, Ch. 6, p. 15

Formulas

8 formulas — click to collapse

Angular momentum

L = r \times p; L = I ω

For a particle: L = r x p. For a rigid body about its rotation axis: L = I omega. Vector quantity.

Symbol	Quantity	SI Unit
L	angular momentum	kg*m^2/s
I	moment of inertia	kg*m^2
omega	angular velocity	rad/s

Valid when

Reference point/axis chosen
I about same axis as omega

Centre of mass of n-particle system

R_{c m} = \frac{\sum m _{i} r _{i}}{\sum m _{i}}

The position of the centre of mass equals the mass-weighted average of particle positions. For continuous bodies use integral form.

Symbol	Quantity	SI Unit
R_cm	CoM position	m
m_i	mass of i-th particle	kg
r_i	position of i-th particle	m

Valid when

System of point particles or rigid body
Inertial reference frame

Moment of inertia for common rigid bodies

I_{sphere} = \frac{2}{5} M R^{2}; I_{hollow} = \frac{2}{3} M R^{2}; I_{rod,c} = \frac{1}{12} M L^{2}; I_{ring} = M R^{2}; I_{disc} = \frac{1}{2} M R^{2}

Standard moments of inertia about the symmetry axis. For other axes use parallel/perpendicular axes theorems.

Symbol	Quantity	SI Unit
M	mass	kg
R	radius	m
L	length	m
I	moment of inertia	kg*m^2

Valid when

Uniform mass distribution
Rotation about symmetry axis (unless noted)

Parallel axes theorem

I = I_{c m} + M d^{2}

Moment of inertia about any axis = moment about parallel axis through CM + Md^2.

Symbol	Quantity	SI Unit
I	MOI about given axis	kg*m^2
I_cm	MOI about parallel CM axis	kg*m^2
M	total mass	kg
d	perpendicular distance	m

Valid when

Both axes parallel
I_cm known about CM axis

Perpendicular axes theorem (planar)

I_{z} = I_{x} + I_{y}

For planar lamina: MOI about axis perpendicular to plane = sum of MOI about two perpendicular in-plane axes through same point.

Symbol	Quantity	SI Unit
I_z	MOI perp to plane	kg*m^2
I_x, I_y	MOI in plane	kg*m^2

Valid when

Body is planar (2D lamina)
All three axes intersect at one point

Rotational kinematic equations (constant alpha)

ω = ω_{0} + α t; θ = ω_{0} t + \frac{1}{2} α t^{2}; ω^{2} = ω_{0}^{2} + 2 α θ

Rotational analogues of linear kinematic equations under constant angular acceleration.

Symbol	Quantity	SI Unit
omega	angular velocity	rad/s
alpha	angular acceleration	rad/s^2
theta	angular displacement	rad
t	time	s

Valid when

Constant alpha
Single rotation axis

Rotational kinetic energy

K E_{rot} = \frac{1}{2} I ω^{2}

Energy of rotation about an axis. Adds to translational KE for rolling bodies.

Symbol	Quantity	SI Unit
I	moment of inertia	kg*m^2
omega	angular velocity	rad/s

Valid when

Rotation about fixed axis
I and omega about same axis

Torque (moment of force)

τ = r \times F

Cross product of position vector and force vector. Magnitude r F sin(theta).

Symbol	Quantity	SI Unit
tau	torque	N*m
r	position from pivot	m
F	force	N
theta	angle between r and F	rad

Valid when

Rigid body or extended object
r measured from chosen pivot/axis

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

7 items — click to collapse

Trap

Centre of mass: equal-distance default

Category: Overthinking

Student answers L/2 for two-particle CoM regardless of mass ratio.

When it triggers

Question gives two masses on rigid rod and asks for CoM distance.

How to avoid

R_cm from m1 = m2*L/(m1+m2). Heavier mass pulls CoM closer to it.

Trap

Angular momentum vs rotational KE conservation

Category: Similar Terms

Student conserves rotational KE when angular momentum is conserved (or vice versa). When I changes, L = Iω is conserved but KE = ½Iω² is NOT (it depends on I and ω together).

When it triggers

Question describes a body whose moment of inertia changes (skater pulling arms in, star collapsing).

How to avoid

L conservation requires zero external torque. KE conservation requires no work done — different criteria. When I changes via internal forces, L conserved, ω increases, KE increases.

Trap

MOI coefficient swap (solid vs hollow)

Category: Similar Terms

Student confuses 2/5 (solid sphere) with 2/3 (hollow sphere) or 1/2 (disc) with 1 (ring).

When it triggers

Question gives a specific geometry and asks for I or radius of gyration.

How to avoid

Memorise: solid sphere 2/5, hollow sphere 2/3, disc/cylinder 1/2, ring/hoop 1, rod-centre 1/12, rod-end 1/3.

Trap

RPM vs rad/s confusion

Category: Unit Conversion

Student plugs rpm directly into formulas requiring rad/s. 1 rpm = 2π/60 rad/s.

When it triggers

Question gives ω in rpm and asks for kinematic quantities in SI units.

How to avoid

Convert: ω(rad/s) = (2π/60) × rpm. Always check units before substituting.

Mistake

Conserves rotational KE when only L is conserved (or vice versa) when MOI changes.

Root cause: concept gap

Correction

L = Iω is conserved when external torque is zero. KE = ½Iω² is NOT conserved when I changes (since ω changes too). When skater pulls arms in, L conserved, ω increases, KE increases (work done by muscles).

Mistake

Confuses MOI coefficients (e.g. solid sphere 2/5 vs hollow sphere 2/3).

Root cause: concept gap

Correction

Memorise standard moments of inertia. Solid sphere has more mass near axis (smaller MOI = 2MR²/5); hollow sphere has all mass at radius R (larger MOI = 2MR²/3).

Mistake

Plugs ω in rpm directly into kinematic formulas requiring rad/s.

Root cause: unit error

Correction

Convert: ω(rad/s) = (2π/60) × ω(rpm). For example, 1200 rpm = 1200 × 2π/60 = 125.66 rad/s.

Past Year Questions

10 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys. — click to collapse

NEET 2025

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

1108 days

2100 days

3105 days

4115 days

NTA Answer: Option 1(final)

NEET 2024Revised key

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly:

18.5 cm

217.5 cm

320.7 cm

472.0 cm

NTA Answer: Option 1(revised_final)

NEET 2024Revised key

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is ν in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)?

1Point P moves slower than point Q

2Point P moves faster than point Q

3Both the points P and Q move with equal speed

4Point P has zero speed

NTA Answer: Option 2(revised_final)

NEET 2023

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is

15 : 3

22 : 5

35 : 2

43 : 5

NTA Answer: Option 5(final)

NEET 2023

The angular acceleration of a body, moving along the circumference of a circle, is

1Along the radius towards the centre

2Along the tangent to its position

3Along the axis of rotation

4Along the radius, away from centre

NTA Answer: Option 3(final)

NEET 2022

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1- 3 - 1 : 2

22 : 1

32 : 1

44 : 1

NTA Answer: Option 3(final)

NEET 2022

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is 10

15 m

2m 3

3- 4 - 2 0 3 m

410 m

NTA Answer: Option 3(final)

NEET 2022

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is

1104

22

34

412

NTA Answer: Option 3(final)

NEET 2021

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' 'MR2'. times Then the value of 'K' is 1

18 3

24 7

38 1

NTA Answer: Option 2(final)

NEET 2021

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in m/s2) equilibrium. (g = 10 20 cm 40 cm 160 cm 0 m 2 kg 1

1kg 12 1

2kg 2 1

3kg 3 1

4kg 6

NTA Answer: Option 1(final)

How NEET usually asks this

4 recurring patterns from past papers — click to collapse

Flywheel undergoing uniform angular acceleration; given initial/final omega and time, find alpha or theta.

Direct ApplicationEasy

Common distractors

forgets conversion rpm to rad s

Treats rpm as rad/s without 2*pi/60 conversion

Two-particle system on a rigid massless rod; find distance of CM from one of the masses. R_cm from m1 = m2*L/(m1+m2).

Direct ApplicationEasy

Common distractors

uses equal distribution

Default to L/2 regardless of mass ratio

Body's angular speed changes when its moment of inertia changes (e.g. star collapses, skater pulls in arms). Apply L = I*omega = constant when no external torque.

Multi StepMedium

Common distractors

uses energy conservation instead

Confusing L conservation with KE conservation

Compare moments of inertia (or radii of gyration) of two standard rigid bodies (e.g. solid sphere vs hollow sphere; disc vs ring) about their natural axes. Apply tabulated I formulas; take ratio.

Direct ApplicationEasy

Common distractors

swap solid hollow coefficients

Confusing 2/5 (solid sphere) with 2/3 (hollow sphere)

Test yourself on this topic with real past-paper questions:

Practice this topic →

Conservation Angular Momentum Moment of Force

Free NEET study resources

Get a structured 30-day Mechanics plan and a complete formula booklet — delivered to your inbox instantly.

Linear vs Rotational Comparison

Lesson

Practice MCQs

Quick recall before you leave

Rotational kinetic energy

Angular momentum

Newton's second law (rotational form)

Rotational kinematic equation

Worked Example

Before solving, remember these

Formulas

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Exam Traps & Common Mistakes

When it triggers

How to avoid

When it triggers

How to avoid

When it triggers

How to avoid

When it triggers

How to avoid

Correction

Correction

Correction

Past Year Questions

How NEET usually asks this

Common distractors

Common distractors

Common distractors

Common distractors

Free NEET study resources