Rotational Motion In the real world there is motion more complicated than left, right, up, and down.  For this we have rotational motion.  It has a direct relation to linear motion as can be seen by the table here to the right. Like linear motion and energy, rotational motion must be conserved. This second point is where things get interesting.  A common example of conservation of rotational momentum is when figure skaters spin.  As shown here:                         Notice she starts with her arms and legs very far out from her body, but by the third and fourth steps she has brought her arms and legs in close.  She does this to increase the speed of her spin and the following equation explains why. L is rotational momentum, r is the radial distance from the center of the spin to the outermost edge of the spinning object, m is the mass of the object and v is the linear velocity of any particle that is rotating with the the object.  According to the Law of Conservation of Angular Momentum: L for the system, or the rotational momentum in a system over a set period of time must remain constant as long as there is no external torque on the system.  This means that r and mv can change but their cross product must always remain the same.  Lets assume that r=1.4m, m=65kg, and v=2m/s.  L would then have to equal 182 kg*m^2/s also known as Newton Meter Seconds (NmS).  182=1.4 x 65*2 Now L has to remain the same because there is no external force on the skater.  So, when she brings her arms in assume that r becomes approximately .7m.  The rest of the equation must adjust as well.  The skaters mass is more or less a constant in this instance, so the only other variable that can change is v. 182=.7 x 65*v   This means the velocity of her spin is now 4 meters per second. Index Home Page 2 Page 3  Bibliography