• In degrees, once around a circle is 360°

• In radians, once around a circle is 2π

• A radian measures a distance around an arc equal to the length of the arc's radius

# Kinematic Variable Parallels

Variable Translational Angular
Displacement Δs Δθ
Velocity v
Acceleration a
Time t t

# Variable Translations

Variable Translational Angular
Displacement <img src="./media/image185.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image185.png"/ <img src="./media/image186.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image186.png"/
Velocity <img src="./media/image187.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image187.png"/ <img src="./media/image188.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image188.png"/
Acceleration <img src="./media/image189.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image189.png"/ <img src="./media/image190.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image190.png"/
Time <img src="./media/image191.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image191.png"/ <img src="./media/image192.png" alt="C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image192.png"/

# Example: Wheel in Motion

• A wheel of radius r and mass M undergoes a constant angular acceleration of magnitude ⍺.

• What is the speed of the wheel after it has completed on complete turn, assuming it started from rest?