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

**ω**rpm = 0.0167 rpm.

_{minuite}= 60^{-1}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

**ΔΔ = ω**. We eliminate the time from the equation for the angular velocity t = (

_{ave}t = ω_{0}+ at^{2}/2**ω – ω**, so that

_{0}) / α**ΔΔ = ω**, We thus arrive at the kinematics equation for rotation,

_{ave}t = (w_{0}+w)/2 * (w_{0}+w)/αWe 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).