Angular displacement is defined,

**Δθ = (arc length / radius) = s/r**

For a full circle θ = 2π rad. Note that rad is not a unit, but rather a placeholder. Thus, “rad” may appear and disappear from equations. The angular velocity is defined:

**ω = Δθ/Δt → (ω) = rad/s**

and angular acceleration,

**α = Δω/Δt → (α) = rad/s ^{2}**

If T is the period, i.e., the time for one revolution is the average speed and is given by,

**ω _{ave} = 2π red / T**

**Solution**

We have the period for the second hand T_{second} = 60 s, so that

**Discussion:** Another unit for angular speed in common use is revolutions per minute (rpm). Then **ω _{second} = 1** rpm and

The Rotational kinematics equations are derived the same way as in the case of linear equations. For **α = const**, we find the average velocity **ω _{ave} = (ω_{0} + ω)/2 = (ω_{0} + αt/2),** so that for the angular displacement we have

We note that these equations are identical to Equations, when quantities for linear motion (x, v, a) are replaced by the respective quantities for rotational motion (θ, ω, α).