Angular Momentum of a Particle
The angular momentum of a particle about origin O is L_O = r cross p, so its magnitude is mvr_perpendicular and can change even at constant speed if the direction or line of motion changes.
Why this shows up in the exam
Particles passing an offset point · Orbital motion under central forces · Choosing an origin for collision analysis
Learn the idea
A particle's angular momentum depends on its linear momentum and its perpendicular offset from the origin. A particle's angular momentum depends on its linear momentum and its perpendicular offset from the origin. 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: Angular momentum is momentum times perpendicular miss distance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- L_O = r cross p — Particle angular momentum about O.
- |L_O| = m v b — Magnitude for impact parameter b relative to O.
- tau_O = dL_O/dt — Torque-angular-momentum relation in an inertial frame.
How to approach it
- 1Name the origin
- 2Find r and momentum at the same instant
- 3Use the cross product or impact parameter with sign
Common slip-ups that cost marks
- •Using radial distance instead of perpendicular distance
- •Assuming L is origin-independent
- •Dropping the cross-product direction
🌟 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.