Angular velocity, velocity, and angular momentum for rotation about a fixed axis.


W – angular velocity; m – angular speed; R,T,P – radius and angles specifying position X; M – mass;

m=slider([0,1])

s=slider([0,1])

R=slider([0,10])

T=pi*s,P=m*n

W=vector(0,0,m)

function(X,R,T,P)=vector(sin(T)*cos(P),sin(T)*sin(P),cos(T))*R

function(V,R,T,P)=cross(W,function(X,R,T,P))

Axis of rotation:

vector(x,y,z)=vector(0,0,10*t-5)

vector(0,0,0),W

function(X,R,T,P)

function(X,R,T,t*P)

vector(0,0,0),function(X,R,T,m*n)

function(X,R,T,P),function(V,R,T,P)+function(X,R,T,P)


M – mass; L – angular momentum;

M=1,function(p,R,T,P)=function(V,R,T,P)*M

function(L,R,T,P)=cross(function(X,R,T,P),function(p,R,T,P))

Angular momentum of this particle. Note that it is not constant and not parallel to the angular velocity. (It is easy to see that the component along the angular velocity is constant, however.)

vector(0,0,0),function(L,R,T,P)

Add a mass at the other end:

function(X,R,T+pi,P)

vector(0,0,0),function(X,R,T+pi,P)

vector(0,0,0),function(L,R,T,P)*2



Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

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