stylistic:style_transfer, information:extraction
General planar motion

These are the kinematic equations for a particle traversing a path in a plane, described by position r = r (t). They are simply the time derivatives of the position vector in plane polar coordinates using the definitions of physical quantities above for angular velocity ω and angular acceleration α. These are instantaneous quantities which change with time.

The position of the particle is

where ê and ê are the polar unit vectors. Differentiating with respect to time gives the velocity

with radial component dr / dt and an additional component rω due to the rotation. Differentiating with respect to time again obtains the acceleration

which breaks into the radial acceleration d r / dt, centripetal acceleration – rω, Coriolis acceleration 2 ω dr / dt, and angular acceleration rα.

Special cases of motion described by these equations are summarized qualitatively in the table below. Two have already been discussed above, in the cases that either the radial components or the angular components are zero, and the non-zero component of motion describes uniform acceleration.