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Reading

F&C ch 8

Recall

Rotation of a Rigid Body About a Fixed Axis

Angular Velocity Vector

Consider an object rotating about the origin in the x-y plane with angular velocity w. Let's pick a point on the body, labelled by i, at location r_i = r_icosq i + r_isinq j = x_i i + y_i j . This point will have a velocity v_i which must be perpendicular to r_i and a magnitude of v_i = wr_i such that we can write v_i = -v_i sinq i + v_i cosq j = w(-r_i sinq i + r_i cosq j) = w(-y_i i + x_i j). But if we say that angular velocity is a vector -- and why not, both velocity and angular momentum are vectors -- then writing w = wk, we see that w×r_i = w(-y_i i + x_i j) = v_i.

Angular Momentum and Moment of Inertia

Kinetic Energy of Rotation

Correspondance between laws of motion for translation and rotation:

© 11 March 1999 R. Harr