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Rotation & Angular Dynamics · Physics

Angular momentum is the “quantity of rotation.”

Angular momentum tracks how rotation is distributed and how hard it is to change. It has a direction, depends on the axis you choose, and connects directly to torque.

This topic

Angular Momentum

Define L carefully, understand its direction, and learn the torque connection that drives conservation ideas.

Definition
What angular momentum means
Angular momentum is a vector that describes rotational motion about a point or axis. Its definition depends on the system and what is rotating.
  • Core idea: “how hard it is to change rotation”
  • Depends on choice of origin/axis
  • Vector direction encodes rotation axis
  • Units: kg·m²/s
Start nano-lesson Always specify the axis or point.
Vector
Direction and the right-hand rule
Angular momentum points along the rotation axis. Use the right-hand rule consistently to set signs and directions in problems.
  • Right-hand rule for rotational direction
  • Positive/negative convention about an axis
  • Common sign mistakes and how to avoid them
  • When L is not along ω (preview)
Start nano-lesson Pick a positive axis and stick with it.
Connection
Torque changes angular momentum
Net external torque is the rotational cause of change in angular momentum. This is the rotational analogue of F = dp/dt.
  • Core link: Στ = dL/dt (about an axis)
  • Impulse-like idea: angular impulse changes L
  • Why external vs internal matters
  • Sets up conservation when Στ ≈ 0
Start nano-lesson Torque is the “rate of change” driver.
Axis choice
Choosing the right origin or axis
The same physical situation can have different angular momentum values about different points. A smart axis choice often makes external torques vanish.
  • Why L depends on the reference point
  • Choosing an axis where torques are simple
  • Common choices: center of mass, pivot point
  • What must stay fixed in “before–after” problems
Start nano-lesson Axis choice can make conservation usable.
Practice
Practice & Exercises
Practice identifying angular momentum direction, using Στ = dL/dt conceptually, and selecting smart axes in problems.
  • Right-hand rule direction drills
  • Determine sign of L and τ about an axis
  • Conceptual: when does torque change L?
  • Axis-choice prompts (which point makes τ small?)
  • Exam-style angular momentum fundamentals sets
Open practice sets Write the axis and sign convention first.