Make AngularVelocity a derivative of Angle

shared/src/main/scala/squants/motion/AngularVelocity.scala

@@ -9,7 +9,8 @@
 package squants.motion
 
 import squants._
-import squants.space.{ Degrees, Gradians, Turns }
+import squants.space.{Degrees, Gradians, Turns}
+import squants.time.TimeDerivative
 
 /**
  * @author  garyKeorkunian
@@ -19,14 +20,17 @@ import squants.space.{ Degrees, Gradians, Turns }
  *
  */
 final class AngularVelocity private (val value: Double, val unit: AngularVelocityUnit)
-    extends Quantity[AngularVelocity] {
-  // TODO - Make this a TimeDerivative of Angle
+    extends Quantity[AngularVelocity] with TimeDerivative[Angle] {
   def dimension = AngularVelocity
 
   def toRadiansPerSecond = to(RadiansPerSecond)
   def toDegreesPerSecond = to(DegreesPerSecond)
   def toGradsPerSecond = to(GradsPerSecond)
   def toTurnsPerSecond = to(TurnsPerSecond)
+
+  protected[squants] def timeIntegrated: Angle = Radians(toRadiansPerSecond)
+
+  protected[squants] def time: Time = Seconds(1)
 }
 
 object AngularVelocity extends Dimension[AngularVelocity] {

shared/src/main/scala/squants/space/Angle.scala

@@ -9,7 +9,8 @@
 package squants.space
 
 import squants._
-import squants.time.Time
+import squants.motion.{AngularVelocity, RadiansPerSecond}
+import squants.time.{Time, TimeIntegral}
 
 /**
  * @author  garyKeorkunian
@@ -18,7 +19,7 @@ import squants.time.Time
  * @param value value in [[squants.space.Radians]]
  */
 final class Angle private (val value: Double, val unit: AngleUnit)
-    extends Quantity[Angle] {
+    extends Quantity[Angle] with TimeIntegral[AngularVelocity] {
 
   def dimension = Angle
 
@@ -34,6 +35,10 @@ final class Angle private (val value: Double, val unit: AngleUnit)
   def tan = math.tan(toRadians)
   def asin = math.asin(toRadians)
   def acos = math.acos(toRadians)
+
+  protected def timeDerived: AngularVelocity = RadiansPerSecond(toRadians)
+
+  override protected def time: Time = Seconds(1)
 }
 
 object Angle extends Dimension[Angle] {

shared/src/test/scala/squants/motion/AngularVelocitySpec.scala

@@ -12,6 +12,7 @@ import org.scalatest.{ Matchers, FlatSpec }
 import scala.language.postfixOps
 import squants.space.Radians
 import squants.QuantityParseException
+import squants.time.Seconds
 
 /**
  * @author  garyKeorkunian
@@ -53,6 +54,10 @@ class AngularVelocitySpec extends FlatSpec with Matchers {
     TurnsPerSecond(1).toString(TurnsPerSecond) should be("1.0 turns/s")
   }
 
+  it should "return Angle when multiplied by Time" in {
+    RadiansPerSecond(1) * Seconds(1) should be(Radians(1))
+  }
+
   behavior of "AngularVelocityConversions"
 
   it should "provide aliases for single unit values" in {

shared/src/test/scala/squants/space/AngleSpec.scala

@@ -10,6 +10,8 @@ package squants.space
 
 import org.scalatest.{ FlatSpec, Matchers }
 import squants.QuantityParseException
+import squants.motion.RadiansPerSecond
+import squants.time.Seconds
 
 /**
  * @author  garyKeorkunian
@@ -75,6 +77,14 @@ class AngleSpec extends FlatSpec with Matchers {
     Radians(1).asin should be(math.asin(1))
   }
 
+  it should "return AngularVelocity when divided by Time" in {
+    Radians(1) / Seconds(1) should be(RadiansPerSecond(1))
+  }
+
+  it should "return Time when divided by AngularVelocity" in {
+    Radians(1) / RadiansPerSecond(1) should be(Seconds(1))
+  }
+
   behavior of "AngleConversion"
 
   it should "provide aliases for single unit values" in {

shared/src/test/scala/squants/space/SpaceChecks.scala

@@ -11,7 +11,7 @@ package squants.space
 import org.scalacheck.Prop._
 import org.scalacheck.Properties
 import squants.QuantityChecks
-import squants.motion.CubicMetersPerSecond
+import squants.motion.{CubicMetersPerSecond, RadiansPerSecond}
 import squants.time.Seconds
 
 /**
@@ -22,6 +22,7 @@ import squants.time.Seconds
 object SpaceChecks extends Properties("Space") with QuantityChecks {
 
   implicit val tolVfr = CubicMetersPerSecond(tol)
+  implicit val tolAngularVelocity = RadiansPerSecond(tol)
 
   property("Area = Length * Length") = forAll(posNum, posNum) { (length1: TestData, length2: TestData) ⇒
     SquareMeters(length1 * length2) == Meters(length1) * Meters(length2) &&
@@ -41,4 +42,11 @@ object SpaceChecks extends Properties("Space") with QuantityChecks {
       Seconds(time) =~ CubicMeters(vfr * time) / CubicMetersPerSecond(vfr) &&
       CubicMetersPerSecond(vfr) =~ CubicMeters(vfr * time) / Seconds(time)
   }
+
+  property("Angle = AngularVelocity * Time") = forAll(posNum, posNum) { (angularVel: TestData, time: TestData) ⇒
+    Radians(angularVel * time) == RadiansPerSecond(angularVel) * Seconds(time) &&
+      Radians(angularVel * time) == Seconds(time) * RadiansPerSecond(angularVel) &&
+      Seconds(time) =~ Radians(angularVel * time) / RadiansPerSecond(angularVel) &&
+      RadiansPerSecond(angularVel) =~ Radians(angularVel * time) / Seconds(time)
+  }
 }