Rotational Equations of Motion
Rotation
12
JEE Qs
8%
Hard
60
min
Master the direct analogy between linear and rotational kinematics; this allows for rapid problem-solving by leveraging familiar linear motion strategies.
🧮 Key Formulas
✅ Key Points for JEE
- 1These equations are direct analogues of the linear kinematic equations (v = u + at, etc.), replacing linear variables (s, u, v, a) with their rotational counterparts (θ, ω₀, ω, α).
- 2The rotational equations of motion are applicable ONLY when the angular acceleration (α) is constant. If α varies, calculus (integration) must be used.
- 3Ensure consistent units: angular displacement (θ) in radians, angular velocity (ω, ω₀) in rad/s, and angular acceleration (α) in rad/s². Convert revolutions to radians (1 revolution = 2π radians).
- 4Pay attention to the sign conventions: Clockwise rotation is often taken as negative, and counter-clockwise as positive, or vice-versa, but be consistent throughout a problem. If ω and α have opposite signs, the body is slowing down.
- 5These equations describe the purely rotational motion of a rigid body about a fixed axis or about its center of mass.
⚠️ Common Mistakes
- ✕Mixing linear kinematic equations with rotational variables, or confusing linear and angular quantities within the same problem (e.g., using 'v' instead of 'ω').
- ✕Applying these equations when angular acceleration is not constant; neglecting to use calculus for variable angular acceleration problems.
- ✕Incorrectly converting units (e.g., leaving angular velocity in RPM or RPS instead of converting to rad/s).
- ✕Ignoring proper sign conventions for angular displacement, velocity, and acceleration, leading to errors in direction or final values.
- ✕Assuming an object starts from rest (ω₀ = 0) or comes to a stop (ω = 0) without explicit information.
📝 Practice Questions
See allQ28.A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in 2025 (22 Jan Shift 1) JEE Main Previous Year Paper the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above. (1) 32 7 MR2 (2) 329 MR2 (3) 17 32 MR2 (4) 1332 MR2
Q48.The position vectors of two 1 kg particles, (A) and (B), are given by→rA = (α1t2^i + α2t^j + α3t^k)m , respectively; →rB = (β1t^i + β2t2^j + β3t^k)m (α1 = 1 m/s2, α2 = 3nm/s, α3 = 2 m/s, β1 = 2 m/s, β2 = −1 m/s2, β3 = 4pm/s), where t is time, n and p −→ are constants. At t = 1 s, VA = →VB and velocities →VA and →VB of the particles are orthogonal to each other. At t = 1 s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is √Lkgm2 s−1 . The value of L is _______ .
Q28.The torque due to the force (2^i + ^j + 2^k) about the origin, acting on a particle whose position vector is (^i + ^j + ^k), would be (1) ^i −^k (2) ^i + ^k (3) ^j + ^k (4) ^i −^j + ^k
Q49.A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is in SI unit. The value of α is __________. √FαM
Q45.A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30∘ with the horizontal. The speed of the particle at the bottom of the plane is v1 . If the angle of inclination is increased to 45∘ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v2 . The ratio v21 : v22 is (1) 1 : √2 (2) 1 : √3 (3) 1 : 3 (4) 1 : 2 2025 (23 Jan Shift 1) JEE Main Previous Year Paper
Q40.A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination 45∘ . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be (1) 1 g (2) 1 g √2 3√2 (3) √2 g (4) √2g 3
NCERT Chapters
- Class 11 Physics Ch 3: Motion in a Straight Line
- Class 11 Physics Ch 7: System of Particles and Rotational Motion