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Angular velocity ω


For counterclockwise uniform circular motion in the x-y plane we found at page 5 an expression for the position vector r(t) and, moreover, at page 6 an expression for the velocity vector v(t), respectively given by

r(t) = (
R cos(ωt)
R sin(ωt)
0
)   and   v(t) = (
-ωR sin(ωt)
ωR cos(ωt)
0
)

The vector product of r(t) and v(t) is given by

r(t) × v(t) = (
0
0
ωR2 cos2(ωt) + ωR2 sin2(ωt)
) = (
0
0
ωR2
)

Hence, r(t) × v(t) is independent of the instant of time t and moreover proportional to ω:

r(t) × v(t) = R2 ω = |r(t)|2 ω



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