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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 ri = ricosq i + risinq j = xi i + yi j . This point will have a velocity vi which must be perpendicular to ri and a magnitude of vi = wri such that we can write vi = -vi sinq i + vi cosq j = w(-ri sinq i + ri cosq j) = w(-yi i + xi 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 wŚri = w(-yi i + xi j) = vi.

Angular Momentum and Moment of Inertia

 

Kinetic Energy of Rotation

 

Correspondance between laws of motion for translation and rotation:

relation translational motion rotational motion
momentum px = mvx Lz = Izw
kinetic energy T = 1/2 mv2 T = 1/2 Izw
equation of motion Fx = dpx/dt Nz = dLz/dt

© 11 March 1999 R. Harr