Conservation of Angular Momentum
For a chosen system and origin, angular momentum is conserved over an interval if the net external angular impulse about that origin vanishes, even though internal torques may redistribute spin.
Why this shows up in the exam
A person pulling arms inward while spinning · Discs brought into rotational contact · Collisions about a frictionless pivot
Learn the idea
Total angular momentum about an origin stays constant when the external torque about that origin is zero. Total angular momentum about an origin stays constant when the external torque about that origin is zero. 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: No outside twist means spin momentum stays.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- L_i = L_f — Conservation when net external angular impulse is zero.
- I_i omega_i = I_f omega_f — Common fixed-axis form when the rotating system changes inertia.
How to approach it
- 1Define the complete system and origin
- 2Check external angular impulse
- 3Equate total initial and final angular momentum, then treat energy separately
Common slip-ups that cost marks
- •Conserving rotational kinetic energy in an inelastic coupling
- •Ignoring external torque about the chosen origin
- •Leaving part of the interacting system out
🌟 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.