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Rotational Motion revision notes

Every idea in the Rotational Motion chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 35 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Rotational kinematics and torque

Rotational kinematics
10× asked, last 2026
ω=ω0+αt,θ=ω0t+12αt2,ω2=ω02+2αθ\omega=\omega_0+\alpha t,\qquad \theta=\omega_0t+\tfrac12\alpha t^2,\qquad \omega^2=\omega_0^2+2\alpha\theta
Constant α\alpha only; otherwise ω=dθ/dt\omega=d\theta/dt, α=dω/dt\alpha=d\omega/dt. Links: v=ωrv=\omega r, at=αra_t=\alpha r.
  • Not rpm or cm inside the formulas. Convert: 1 rpm =2π/60=2\pi/60 rad/s, revolutions =θ/2π=\theta/2\pi, cm to m before squaring. Wrong options are often off by 2π2\pi, a factor 2 or a power of ten.
  • Quick method. From rest at constant α\alpha, angles in successive equal intervals go 1:3:5:…1:3:5:\dots. For α(t)\alpha(t), integrate twice with the given ω0,θ0\omega_0,\theta_0; motion reverses only when ω=0\omega=0, not when the force does.
Torque about a point
8× asked, last 2026
τ⃗=r⃗×F⃗,∣τ⃗∣=rFsin⁡θ=F r⊥\vec\tau=\vec r\times\vec F,\qquad |\vec\tau|=rF\sin\theta=F\,r_\perp
r⃗\vec r runs from the reference point to the point where F⃗\vec F acts. r⊥r_\perp = lever arm. Unit N m.
Oline of actionr⃗\vec rF⃗\vec Fr⊥=rsin⁡θr_\perp=r\sin\thetaθ\theta
τ=rFsin⁡θ=F r⊥\tau=rF\sin\theta=F\,r_\perp: the force times its lever arm
  • A couple (equal, opposite, parallel forces dd apart) has zero net force and the same torque FdFd about every point: it only rotates.
  • Not r⃗\vec r from the origin when torque is asked about another point: use r⃗=r⃗force−r⃗point\vec r=\vec r_{\text{force}}-\vec r_{\text{point}}. The same force has a different torque about each point.
  • Quick method. In the xyxy-plane τz=xFy−yFx\tau_z=xF_y-yF_x (same for LzL_z with p⃗\vec p). In 3D write the determinant and find only the component asked.

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Practise Rotational Motion

33 more concepts in 6 topics

Moment of inertia, Parallel and perpendicular axis theorems, Rotational dynamics and energy, Angular momentum and its conservation, Rolling motion and Equilibrium of rigid bodies. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Moment of inertia

  • Moment of inertia and radius of gyration17×
  • Rod, ring and disc17×
  • Spheres and cylinders20×
  • Cylinder across its axis, plate, cone7×
  • Same material, different size8×

Parallel and perpendicular axis theorems

  • Parallel axis theorem9×
  • Perpendicular axis theorem7×
  • Tangent and rim axes6×
  • Composite bodies14×
  • Removed portion5×

Rotational dynamics and energy

  • Linear and rotational analogues
  • Torque and angular acceleration12×
  • Pulley with mass5×
  • Energy method for a falling block6×
  • Rotational KE, work and power7×
  • Rod hinged at one end, released5×

Angular momentum and its conservation

  • Angular momentum of a particle7×
  • Projectile about the launch point3×
  • Angular momentum of a rigid body6×
  • Conservation of angular momentum8×
  • Two discs coupled7×
  • Particle striking a pivoted rod4×
  • Angular impulse4×

Rolling motion

  • Rolling without slipping3×
  • Kinetic energy of rolling11×
  • Rolling down an incline16×
  • String unwinding (yo-yo)1×
  • Rolling up a slope or curve5×
  • Force applied to a rolling body2×
  • Rolling with slipping2×

Equilibrium of rigid bodies

  • Conditions of equilibrium5×
  • Ladder against a wall1×
  • Toppling and climbing a step1×

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