Angular Momentum

What this investigation asks

A spinning system can change speed when its shape changes without receiving an equivalent new external angular impulse. This investigation follows angular momentum as rotational inertia and interactions change. Identify the axis and include every relevant part of the system before predicting a result. A single rotating component can gain or lose angular momentum through interactions with another component even when the combined total remains unchanged. The goal is to connect measured rotation to a system account rather than treating faster spin as automatic evidence that angular momentum increased.

Design and measure the comparison

Compare a rotating arrangement with masses at different distances from the axis. Keep the total participating mass and external conditions explicit. Moving mass inward changes rotational inertia, so a conserved total angular momentum requires a corresponding angular-speed change. Record the before and after geometry with the speeds instead of reporting only a speed ratio. In the spin-up activity, retain the applied torque and its duration. Equal angular impulses can produce different final speeds when the objects have different rotational inertias.

Connect the record to the model

Use rotational inertia multiplied by angular velocity to calculate angular momentum about the selected axis. The area under a torque-time record gives angular impulse, and the slope of angular momentum versus time describes the net external torque. Compare those relationships with the measured event. When a ring lands on a disk, account for both components before and after contact. Their contact torques are opposite, so their contact angular impulses cancel in the combined system. That cancellation does not require each component's angular momentum to remain unchanged during the interaction.

Interpret the evidence and its limits

Distinguish angular-momentum conservation from mechanical-energy conservation in an inelastic contact or shape-change event. A contact can redistribute rotation and dissipate mechanical energy while preserving the combined angular momentum under negligible external torque. In the Real comparison, bearing effects can change the total more slowly. Retain the time interval when assessing that drift. A final explanation should name the system, external torque assumptions, and geometry change, then compare both the total and component records. Do not use a component's loss alone as evidence that the complete system has violated conservation.

Reference conditions and quantities

For the course rotating-chair reference, rotational inertia changes from 3.45 to 1.36 kg·m². Under the specified negligible-external-torque condition, use those inertias to predict the corresponding speed ratio at constant angular momentum. The values describe this arrangement; the change in rotational kinetic energy requires its own account and is not determined by a conservation statement for angular momentum alone.

Use the record to test your explanation

Write a prediction before collecting the comparison, naming the quantity that should change and the condition you will alter. Keep a reference run and vary one factor at a time when the question calls for a controlled test. Record the selected apparatus settings, units, and measurement interval. Where an activity supplies Ideal and Real modes or seeded variation, retain that identity with each record rather than mixing incompatible runs in one calculation.

Separate an instrument reading or counted observation from the model relationship used to explain it. Keep raw values alongside derived results so another student can reconstruct the argument. A graph needs labeled axes and a stated comparison range. If a result differs from a reference, inspect the conditions, rounding, and measurement procedure before changing the explanation.

For a classroom discussion, compare claims supported by the same evidence and identify an additional measurement that would distinguish competing accounts. Finish with a claim, the relevant observations, and reasoning tied to this course's model. State a specific limitation instead of assigning a general error label to every disagreement.

Related investigations

Compare the no-slip rotation in Rolling Race, then examine torque balance in Torque & Balance. State whether the question concerns a static equilibrium, an applied angular impulse, or a change in the geometry of a rotating system.