Angular Impulse
Rotation
12
JEE Qs
8%
Hard
45
min
Apply the angular impulse-momentum theorem (ΔL = ∫τ dt) whenever a significant impulsive torque acts on a system for a short duration, directly linking it to the change in angular velocity.
🧮 Key Formulas
✅ Key Points for JEE
- 1Angular impulse is the rotational analogue of linear impulse and is defined as the change in angular momentum (ΔL) of a system.
- 2It is particularly useful for analyzing situations where a large torque acts for a very short duration, such as impacts or sudden forces on a rotating body.
- 3The angular impulse-momentum theorem states that the net angular impulse acting on a system equals the change in its total angular momentum (J_angular_net = L_final - L_initial).
- 4Angular impulse can be calculated by integrating the net torque (τ) with respect to time over the duration of the impulse: J_angular = ∫τ dt.
- 5The direction of angular impulse is the same as the direction of the net torque causing the change in angular momentum, following the right-hand rule for cross products.
⚠️ Common Mistakes
- ✕Confusing angular impulse with torque or linear impulse, failing to recognize its definition as change in angular momentum.
- ✕Incorrectly choosing the axis of rotation for calculating torque and angular momentum, leading to errors in their vector cross products.
- ✕Neglecting the vector nature of torque and angular momentum, especially when dealing with forces that are not perpendicular to the position vector or problems in 3D.
- ✕Incorrectly applying the angular impulse-momentum theorem by not accounting for all external torques acting on the system.
📝 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