Unit: Energy and Momentum of Rotating Systems

Lesson Preview

Angular momentum can change whenever an object experiences a change in angular speed, a change in direction of rotation, or a change in rotational inertia, which could involve a change in mass and/or mass distribution/size.

The change in angular momentum (ΔL\Delta \vec{L}) is the difference between the final angular momentum Lf\vec{L}_f and the initial angular momentum Li\vec{L}_i of an object over some time interval.

ΔL=LfLi\Delta \vec{L} = \vec{L}_f - \vec{L}_i

For a rigid object with constant rotational inertia II, that is to say constant mass and size, the change in angular momentum is directly related to the change in angular velocity Δω\Delta \vec{\omega}.

ΔL=IωfIωi=I(ωfωi)=IΔω\Delta \vec{L}=I\vec{\omega}_f-I\vec{\omega}_i=I\big(\vec{\omega}_f-\vec{\omega}_i\big)=I\Delta \vec{\omega}

The magnitude of change in angular momentum ΔL|\Delta \vec{L}| depends on several scenarios:

If the object speeds up while rotating in the same direction, then ωf>ωi|\omega_f| > |\omega_i| and ΔL=I(ωfωi)|\Delta L| = I(\omega_f - \omega_i).

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... continued in the full lesson.

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