Angular Momentum of a Rigid Body
For rotation about a fixed principal axis, rigid-body angular momentum along that axis is L = I omega; in general three-dimensional rotation, angular momentum need not be parallel to angular velocity.
Why this shows up in the exam
Flywheel angular momentum · Comparing spinning bodies with different inertia · Relating torque to changing spin
Learn the idea
A rigid body's spin angular momentum is tied to its mass distribution and angular velocity. A rigid body's spin angular momentum is tied to its mass distribution and angular velocity. 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: Spin momentum equals rotational inertia times spin rate on a principal axis.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- L_axis = I_axis omega — Rigid-body angular momentum about a fixed principal axis.
- tau_ext = dL/dt — External torque changes total angular momentum.
How to approach it
- 1Specify the axis
- 2Use inertia about that same axis
- 3Check whether vector direction can change
Common slip-ups that cost marks
- •Using L=I omega for an arbitrary non-principal axis
- •Using mass instead of moment of inertia
- •Confusing angular momentum with rotational kinetic 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.