structural:expansion, linguistic:paraphrasing
Kinematic quantities

From the instantaneous position r = r (t), instantaneous meaning at an instant value of time t, the instantaneous velocity v = v (t) and acceleration a = a (t) have the general, coordinate-independent definitions;

Notice that velocity always points in the direction of motion, in other words for a curved path it is the tangent vector. Loosely speaking, first order derivatives are related to tangents of curves. Still for curved paths, the acceleration is directed towards the center of curvature of the path. Again, loosely speaking, second order derivatives are related to curvature.

The rotational analogues are the "angular vector" (angle the particle rotates about some axis) θ = θ (t), angular velocity ω = ω (t), and angular acceleration α = α (t):

where n̂ is a unit vector in the direction of the axis of rotation, and θ is the angle the object turns through about the axis.

The following relation holds for a point-like particle, orbiting about some axis with angular velocity ω:

where r is the position vector of the particle (radial from the rotation axis) and v the tangential velocity of the particle. For a rotating continuum rigid body, these relations hold for each point in the rigid body.