Angular Momentum — L = Iω, conservation
Rotation
12
JEE Qs
8%
Hard
75
min
Always identify the system, the axis of rotation, and check for any external torques before applying angular momentum conservation; often, the axis about which net external torque is zero is the best choice.
🧮 Key Formulas
✅ Key Points for JEE
- 1Angular momentum (L) is a vector quantity; its direction (given by the right-hand rule for r x p or ω) is crucial for vector addition and conservation.
- 2The total angular momentum of a system remains conserved only if the net external torque acting on the system is zero. Internal torques do not change the total angular momentum of the system.
- 3For a rigid body rotating about a fixed axis or an axis passing through its center of mass, L = Iω. If I changes (e.g., due to mass redistribution), ω must change to conserve L.
- 4For point particles or general systems, L = r x p is the fundamental definition. For an extended body, the total angular momentum is the vector sum of angular momenta of its constituent particles.
- 5Angular momentum conservation is a powerful tool to solve problems involving changes in mass distribution or collisions where external torques are negligible about a chosen axis.
⚠️ Common Mistakes
- ✕Confusing the conditions for conservation of linear momentum (net external force = 0) with angular momentum (net external torque = 0).
- ✕Incorrectly identifying the axis about which angular momentum and moment of inertia are calculated, especially in non-fixed axis problems.
- ✕Ignoring the vector nature of angular momentum, leading to errors in problems with multiple rotation axes or changing directions of rotation.
- ✕Applying L = Iω indiscriminately; this formula is for rigid bodies about an axis of symmetry or fixed axis, not always for a point particle or a general system where r x p is more appropriate.
📝 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 7: System of Particles and Rotational Motion