Rotational Motion Quiz & Theory – JEE Main 2026 | NEET JEE Rankers

Rotational Motion – JEE Main 2026

Quiz + Detailed Theory | MCQ + Numerical

Q1. A solid sphere rolls without slipping. If (angular momentum about centre) : (total energy) = π : 22, angular speed (rad/s) is:
Correct Answer: 4
Q2. A solid sphere of mass 2 kg rolls purely with total kinetic energy 2240 J. Velocity of centre of mass (m/s) is:
Correct Answer: 40
Q3. Moment of inertia of a solid disc about its diameter is 2.5 times that of a ring (same axis). Moment of inertia of a solid sphere (same radius & axis) is n times that of the ring. Find n.
Correct Answer: 4
Q4. Moment of inertia of a circular ring (mass M, radius r) about a tangential axis in its plane is:
Q5. Moment of inertia of a semicircular ring about an axis through centre and perpendicular to its plane is (1/x)MR². Find x.
Correct Answer: 1
Q6. A circular disc slides down an incline in time t. If it rolls down, time taken is √(α/2) t. Find α.
Correct Answer: 3
Q7. Two discs of same mass have thicknesses 1 cm and 0.5 cm. Density ratio = 3 : 5. Ratio of their moments of inertia about diameter is x/6. Find x.
Correct Answer: 5
Q8. A circular disc (mass M, radius R) has angular position θ(t) = 5t² − 8t. Power delivered by torque at t = 2 s is:
Q9. A particle is at (1,1,1) m. Force F = i − j + k acts on it. Magnitude of torque about origin along z-direction is:
Correct Answer: 2
Q10. A uniform rod of mass 12 kg rests with one end on ground and other on man’s shoulder making 60° with horizontal. Load experienced by man is:

Rotational Motion – Complete Theory

1. What is Rotational Motion?

Rotational motion is the motion of a rigid body in which all its particles move in circular paths about a fixed axis called the axis of rotation. Examples include a rotating wheel, ceiling fan, rolling sphere, and Earth rotating about its axis.

2. Angular Variables

  • Angular displacement (θ): change in angular position
  • Angular velocity (ω = dθ/dt)
  • Angular acceleration (α = dω/dt)

3. Torque

Torque is the rotational effect of force and is defined as:
τ = r × F
It is the rotational analogue of force in linear motion.

4. Moment of Inertia (I)

Moment of inertia measures the resistance of a body to change in rotational motion and depends on mass distribution about the axis.

  • Ring about centre: MR²
  • Disc about centre: ½MR²
  • Solid sphere: 2/5 MR²
  • Rod about centre: 1/12 ML²

5. Rotational Kinetic Energy

Krot = ½ Iω²

6. Rolling Motion

In pure rolling:
v = ωR
Total kinetic energy:
K = ½ mv² + ½ Iω²

7. Angular Momentum

L = Iω
Conserved if external torque is zero.

8. Power in Rotational Motion

P = τω

Rotational Motion is one of the most important chapters for JEE Main & Advanced due to heavy weightage of numericals and conceptual MCQs.

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