System of Particles and Rotational Motion

Easy Recall (3)Direct Application (3)Calculation (2)

Moment of Inertia Geometry

Easy Recall (3)Direct Application (3)Calculation (2)

Parallel Perpendicular Axes Theorems

Easy Recall (3)Direct Application (3)Calculation (2)

Rotational Equations of Motion

Easy Recall (2)Direct Application (3)Calculation (2)Concept Trap (1)

Torque

8 MCQs4 revision cardsWorked example

Easy Recall (3)Direct Application (3)Concept Trap (1)Calculation (1)

Past-paper questions from this unit

11 questions from NEET 2021, 2022, 2023, 2024, 2025, 2026. Answers verified against NTA official keys.

By year in our set: 2021 (1) · 2022 (3) · 2023 (2) · 2024 (2) · 2025 (1) · 2026 (2)

Lesson: Parallel Perpendicular Axes Theorems

NEET 2026

A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r < R and mass m < M. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of A is I_A and that calculated about a vertical axis passing through the centre of B is I_B. The difference I_A − I_B is :

1(M − m)(R + r)²

2(m − M)(R + r)²

3(m − M)(R − r)²

NTA Answer: Option 2(final)

Report an error · Every fix is public: corrections log

Lesson: Angular Momentum

NEET 2026

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O. Its angular momentum is L_A and L_B computed about points A and B, respectively, with OB = 2 × OA. The value of L_A/L_B is :

11/4

21/2

NTA Answer: Option 3(final)

Report an error · Every fix is public: corrections log

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.

NEET 2025

1108 days

2100 days

3105 days

4115 days

NTA Answer: Option 1(final)

Report an error · Every fix is public: corrections log

Lesson: Moment of Inertia

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)

Report an error · Every fix is public: corrections log

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)

Report an error · Every fix is public: corrections log

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)

Report an error · Every fix is public: corrections log

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)

Report an error · Every fix is public: corrections log

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

11 : √2

22 : 1

3√2 : 1

44 : 1

NTA Answer: Option 3(final)

Report an error · Every fix is public: corrections log

Lesson: Centre of Mass Two Particle

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

15 m

210 m 3

320 m 3

410 m

NTA Answer: Option 3(final)

Report an error · Every fix is public: corrections log

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

NEET 2022

1104π

22π

34π

412π

NTA Answer: Option 3(final)

Report an error · Every fix is public: corrections log

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' times 'MR²'. Then the value of 'K' is

NEET 2021

11/8

23/4

37/8

41/4

NTA Answer: Option 2(final)

Report an error · Every fix is public: corrections log

Exam traps and common mistakes in this unit

Lesson: Centre of Mass Two Particle

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.

Formulas in this unit

Lesson: Angular Momentum

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

Lesson: Centre of Mass Rigid Body

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

Lesson: Linear vs Rotational Comparison

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

Lesson: Moment of Force

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

Lesson: Moment of Inertia

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)

Lesson: Parallel Perpendicular Axes Theorems

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

Lesson: Parallel Perpendicular Axes Theorems

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

NEET question patterns in this unit

Lesson: Centre of Mass Two Particle

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)