Rotation, Moment of Inertia, Torque and all that..

Here are three lectures related to a subject which for good reason has been troubling some students: From rotation of rigid bodies to angular Momentum, moment of Inertia and Torque.  What we usually call “Impulsmomentsætningen” (IMS) is in reality just Newton’s 2. law for rotation, so including Newton’s 2. law

we have the IMS, “Newton’s 2. law for rotation”:

Here is momentum (also called linear momentum), and is angular momentum, and is the moment of Inertia. Remember that the torque of a force is , i.e. a cross-product. In a mechanics problem with rotation, you usually would need both Newton’s 2′nd law and IMS to solve it.

Don’t forget “rolling without slipping” of a body with radius R. In this case, you have:

, and .

The kinetic energy of a body that rolls is,

,

the sum of the rotational kinetic energy and the translational kinetic energy.

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Topics covered in this lecture:

Rotation of rigid bodies — Moment of Inertia — Parallel axis theorem

Topics covered in this lecture:

Angular momentum — Torque — Conservation of angular momentum

Topics covered in this lecture:

Torque — Oscillating bodies