Lesson 5 of 6 · Angular momentum
Track rotation with angular momentum
9 minute lesson · 3 checks along the way
Your goal for this lessonApply angular-momentum conservation about a stated axis and explain the energy source when changing mass distribution changes spin.
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Specify the center and the axis
describes motion about a chosen origin. Both an orbiting object and a spinning body can have angular . The chosen origin matters: a particle passing one point can have a different angular momentum about another. For the simple spin examples here, use an inertial frame centered on the system’s center of mass and a single stated axis through that center.
In a rigid body rotating about a , the angular momentum component is L = Iω. The symbol ω means , measured in radians per second; I is the moment of inertia about that axis. Moment of inertia depends on how mass is distributed, not just its total. A small mass at twice the distance from the axis contributes four times as much to I.
Torque changes the angular-momentum account
measures a force’s turning effect about the chosen origin or axis. A perpendicular force acting farther from an axis produces more torque. Total angular momentum is conserved when net external torque is negligible. Internal torques can transfer angular momentum between components without changing the total. These statements concern the specified system; excluding a motor’s reaction on the spacecraft would hide part of its operation.
Constant angular momentum does not always mean constant rotation rate. If a mechanism pulls masses inward while preserving a common spin axis, I decreases and ω increases. The resulting rotational , K = ½Iω² in this simple model, can increase. The mechanism must supply to draw the moving masses inward. There is no free energy created by the conservation of angular momentum.
Check 1 of 3
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Work through a decision
Reconfigure a fictional spinning instrument
Imagine a symmetric instrument platform with masses that can slide inward. Initially its is 8 kg m² and its angular velocity is 2 rad/s. The complete platform has angular momentum 16 kg m²/s about its spin axis. Neglect external torque. After an internal mechanism reduces I to 4 kg m², conservation requires a final angular velocity of 4 rad/s.
Initial rotational kinetic energy is ½ × 8 × 2² = 16 . Finally it is ½ × 4 × 4² = 32 joules. The extra 16 joules comes from energy supplied by the internal mechanism; losses would require further input. This example moves existing masses within the system. Throwing material away instead requires counting the angular momentum carried away, so the remaining body alone need not retain its original total.
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Do not confuse a launch stack with a free spinner
Ulysses used during its journey to study the Sun. Its deployment photograph shows the departing spacecraft and attached propulsion hardware as an assembly after release from the shuttle. Hardware separation changes which components remain together. A photograph of the stack does not reveal the later observatory’s complete mass distribution, angular velocity, or the angular momentum exchanged during its deployment sequence.
To investigate a real reconfiguration, specify the interval, track departing hardware, and use engineering mass properties and rotation measurements. The inward-sliding platform above is a separate teaching model, not a claim that Ulysses performed that maneuver. This distinction makes conservation useful: the rule stays the same, while the system boundaries and available measurements determine which simplified calculation can responsibly describe a particular event.
Ulysses and its attached propulsion hardware after release from Discovery on October 6, 1990, in NASA photograph STS041-601-009. NASA records a handheld film photograph. The assembly remains small within the preserved square frame; it has not been enlarged into a reconstructed close-up. This is deployment context, not a view of the later free observatory spinning at a measured rate.
Look closely
Notice the attached assembly in the center. Why would the angular momentum of only the later separated observatory require more information than this photograph supplies?
See what to notice
You would need the later mass distribution and measured rotation, plus an account of angular momentum carried by separated hardware and any external torques. A single deployment view does not determine those quantities or justify applying the inward-sliding teaching model to Ulysses.
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Put it together
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