Angular Kinetics

Newton’s laws of motion: Newton’s laws of motion introduced during week 13 can be restated to represent angular kinetic and kinematic relationships. For example, each linear kinetic measure is substituted for an angular kinetic measure (e.g., torque for force).  So, what is the angular version of Newton’s first law of motion?

1. Law of inertia: A rotating body will continue in a state of uniform angular motion unless acted on by an external torque.

 You may recall that inertia (a unitless concept measured by mass) was a measure of a body’s resistance to linear motion (i.e., a massive body will be difficult to move).  The angular equivalent of mass is moment of inertia.  Moment of inertia is a body’s resistance to angular motion and is influenced by a body’s mass and its distribution from some axis of rotation.  The equation below simplifies moment of inertia.

Moment of inertia (I) = mass (m) * radius of gyration squared (k²) or I = m k²   

Where m is the mass of a body and k is the distance from the axis of rotation to a point at which mass of a body is theoretically concentrated (k is not the center of gravity).  Notice in the illustrations below how k is defined from the mediolateral axis of rotation and the mass concentration point from the axis. k is different for each axis of rotation.