Angular Impulse
Angular impulse about an origin is the time integral of external torque about that origin and equals the corresponding change in angular momentum, including impulsive forces during short collisions.
Why this shows up in the exam
Short impacts on rods and discs · Time-varying motor torque · Estimating spin change from an impulse
Learn the idea
Torque accumulated over time produces a finite change in angular momentum. Torque accumulated over time produces a finite change in angular momentum. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: Area under torque-time is change in angular momentum.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- J_angular = integral tau_ext dt = Delta L — Angular impulse-momentum theorem.
- Delta L_O = r cross J — Angular-momentum change from a linear impulse J at position r.
How to approach it
- 1Fix one origin
- 2Integrate torque or take r cross impulse
- 3Relate initial and final angular momentum with consistent signs
Common slip-ups that cost marks
- •Using peak torque instead of integrating
- •Mixing torque origins before and after impact
- •Assuming angular impulse conserves energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
More from Motion of System of Particles and Rigid Body
Conservation of momentum and angular momentum
The total linear and angular momentum of a system remains constant in the absence of external forces or torques, including during collisions and rotational motion.
Moment of inertia and radius of gyration
Moment of inertia quantifies how mass is distributed with respect to an axis of rotation, and the radius of gyration is a measure related to this distribution.
Torque and rotational equilibrium
Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.
Center of mass: definition and calculation
The center of mass is the point representing the mean position of the mass in a system, and can be calculated for discrete particles or continuous bodies.
Rotational kinematics and dynamics
Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.
Centre of Mass of Discrete Particles
For discrete particles, the centre-of-mass position is the vector sum of each mass times its position divided by total mass; this point governs translation even when the particles move relative to one another.