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Q. A particle moves along a circle of radius $R = 1\, m$ so that its radius vector $\vec{r}$ relative to a point on its circumference rotates with the constant angular velocity $\omega=2\, rad/s$. The linear speed of the particle is

Motion in a Plane

Solution:

Angular velocity about center $= 2$ (angular velocity about any point on its circumference)
or $\omega=2 (2)$ rad/s
or $\omega=2$ rad/s
now $ v = r \omega = (1) (4) = 4\, m/s$