Rigid Body Dynamics (Rotational Motion) Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Rigid Body Dynamics & Rotational Motion Class 11 — Competishun
Rigid Body Dynamics (Rotational Motion) Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Rigid Body Dynamics, also known as Rotational Motion or "System of Particles and Rotational Motion", is one of the most important and highest scoring chapters in Class 11 physics for JEE and NEET. It extends everything you learned about linear motion to spinning bodies, using rotational versions of force, mass and momentum.
This page gives you the complete Rigid Body Dynamics formula sheet for Class 11 in one place: rotational kinematics, torque, moment of inertia of common bodies, angular momentum, rotational energy, rolling motion and the axis theorems, with worked examples. Download the free PDF below and keep it handy for revision.
Download the Rigid Body Dynamics Formula Sheet PDF
Get all rotational motion formulas, moment of inertia values, angular momentum and rolling motion in one clean PDF, free. Perfect for Class 11, JEE and NEET revision.
Download Free PDFWhat is Rigid Body Dynamics?
A rigid body is one that does not deform, the distance between any two points stays fixed. Rotational motion studies how such a body spins about an axis. Every linear quantity has a rotational partner: force becomes torque, mass becomes moment of inertia, and linear momentum becomes angular momentum.
Linear vs Rotational Motion (Analogy)
The fastest way to learn this chapter is to see how each rotational quantity mirrors its linear version.
| Linear Quantity | Rotational Quantity |
|---|---|
| Displacement s | Angular displacement θ |
| Velocity v | Angular velocity ω |
| Acceleration a | Angular acceleration α |
| Mass m | Moment of inertia I |
| Force F | Torque τ |
| Momentum p = mv | Angular momentum L = Iω |
| F = ma | τ = Iα |
| KE = ½mv² | KE = ½Iω² |
| Learn one column and the other follows. This analogy makes the whole chapter click. | |
1. Rotational Kinematics
| Equation | Formula |
|---|---|
| First equation | ω = ω₀ + αt |
| Second equation | θ = ω₀t + ½αt² |
| Third equation | ω² = ω₀² + 2αθ |
| Linear-angular link (velocity) | v = rω |
| Tangential acceleration | a_t = rα |
| Centripetal acceleration | a_c = ω²r = v²/r |
| These are exactly the linear kinematic equations with s→θ, v→ω, a→α. | |
2. Torque, Moment of Inertia & Radius of Gyration
| Concept | Formula |
|---|---|
| Torque | τ⃗ = r⃗ × F⃗, τ = rF sinθ |
| Newton's law (rotation) | τ = Iα |
| Moment of inertia | I = Σ m r² |
| Radius of gyration | I = M K², K = √(I/M) |
| Moment of inertia depends on mass AND how that mass is distributed from the axis. | |
3. Moment of Inertia of Common Bodies
These standard values are used constantly. Memorise them.
| Body | Axis | Moment of Inertia |
|---|---|---|
| Ring | Central, ⊥ to plane | M R² |
| Disc | Central, ⊥ to plane | ½ M R² |
| Solid cylinder | Own axis | ½ M R² |
| Solid sphere | Diameter | (2/5) M R² |
| Hollow sphere | Diameter | (2/3) M R² |
| Rod | Centre, ⊥ to length | (1/12) M L² |
| Rod | One end, ⊥ to length | (1/3) M L² |
| Tip: the more spread out the mass, the larger the moment of inertia (ring > disc for same M, R). | ||
4. Axis Theorems
| Theorem | Formula | Applies to |
|---|---|---|
| Parallel axis | I = I_cm + M d² | Any body |
| Perpendicular axis | I_z = I_x + I_y | Planar (flat) bodies only |
| Use the parallel axis theorem to shift the axis; use the perpendicular axis theorem only for flat laminae. | ||
5. Angular Momentum & Rotational Energy
| Concept | Formula |
|---|---|
| Angular momentum | L = Iω = r⃗ × p⃗ |
| Torque-momentum relation | τ = dL/dt |
| Conservation of L | If τ = 0, L = Iω = constant |
| Rotational KE | KE = ½ I ω² |
| Work by torque | W = τθ |
| Rotational power | P = τω |
| Conservation of angular momentum explains why a spinning skater speeds up on pulling their arms in (I decreases, ω increases). | |
6. Rolling Motion
| Concept | Formula |
|---|---|
| Rolling condition | v = Rω |
| Total KE while rolling | KE = ½mv² + ½Iω² |
| KE using K | KE = ½mv² (1 + K²/R²) |
| Acceleration on incline | a = g sinθ / (1 + K²/R²) |
| On an incline, a solid sphere (smaller K²/R²) rolls down faster than a ring (larger K²/R²). | |
Worked Examples
| Problem | Solution |
|---|---|
| MI of solid sphere, M=2, R=0.5 | I = (2/5)(2)(0.5²) = 0.2 kg·m² |
| Torque: I=0.2, α=5 | τ = Iα = 0.2 × 5 = 1 N·m |
| Rot. KE: I=0.2, ω=10 | KE = ½(0.2)(10²) = 10 J |
| v of point, r=0.5, ω=10 | v = rω = 0.5 × 10 = 5 m/s |
| L: I=0.2, ω=10 | L = Iω = 0.2 × 10 = 2 kg·m²/s |
| Every rotational problem mirrors a linear one, just swap the quantities. | |
Common Mistakes to Avoid
- Wrong moment of inertia: MI depends on the axis, always check which axis is given
- Confusing solid and hollow: Solid sphere is (2/5)MR², hollow is (2/3)MR²
- Perpendicular axis misuse: It works only for flat, planar bodies
- Forgetting rolling KE: Rolling has both translational AND rotational KE
- Torque sign: Torque is a vector, note its direction with the right-hand rule
Why This Chapter Matters for JEE & NEET
- High weightage: Rotational motion appears every year in JEE Main, Advanced and NEET
- Concept heavy: Rewards clear understanding of moment of inertia and angular momentum
- Foundation for more: Used in gravitation, SHM and mechanics of rigid bodies
- Scoring once mastered: The analogy method makes it fast and reliable
How to Use This Formula Sheet
- Master the analogy table: It unlocks half the chapter instantly
- Memorise the MI values: Ring, disc, sphere and rod appear again and again
- Practise rolling and incline problems: They combine several ideas
- Revise from the PDF: Skim it before every physics test and mock
Get the Complete Formula Sheet PDF Free
Download the full Rigid Body Dynamics and Rotational Motion Class 11 formula sheet and revise anytime, anywhere.
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Frequently Asked Questions — Rigid Body Dynamics
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