# Angular Motion

Objectives

• Define how to measure and calculate changes in angular position (angular displacement) and the time derivatives angular velocity and angular acceleration
• Apply Newton's Laws of Motion to angular motion
• Use the equations of angular motion and demonstrate how they interact with each other

Describing angular position

Joint and segmental angles

Newton's Laws (applied to angular motion)

• Every body continues in its state of rest, or of uniform angular motion, unless it is compelled to change that state by torques impressed upon it.
• The change of angular motion of an object is proportional to the torque impressed; and is made in the direction of the torque (T=Ia).
• To every action, there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal and directed to contrary parts.
Equations of angular motion Connection of Linear and Angular Velocity:

v = w * r (Golf example)

Tangential Acceleration: The component of of linear acceleration tangent to the circular path of a point on a rotating object

aT = a * r

Centripetal Acceleration: The linear acceleration directed toward the axis of rotation (Hammer throw)

ar = w 2 r

Angular Momentum H=Iw
Angular Inertia I=mk2
Ice-skating spin