One property of matter which we rarely think about, but greatly influences motorcycle design and how they are ridden, is inertia. Yet it is this property that allows engines to run, stops our bikes from falling over and lets us steer them around corners. Newton's first law states that a body at rest will remain at rest and a body in motion will remain in uniform motion in a straight line, unless acted upon by an outside force.
The unwillingness of something to have its state of rest or motion changed is measured by its inertia. (Picture our man "Six-Pack" Brasfield at rest on his couch-he ain't going anywhere-as having a lot of inertia.) For straight-line motion, the inertia of an object is simply its mass or, because we're on earth, its weight. The heavier something is, the more force required to accelerate or stop it (Newton's second law).
For spinning bodies, the moment of inertia takes into account an object's mass as well as how that mass is distributed about the axis of rotation. The higher an object's moment of inertia, the harder it is to turn about an axis. For a point mass (essentially an object without size dimensions, Figure 1), the moment of inertia is:
Where I is the moment of inertia (or MoI which is measured in lb ft2), m is the object's mass (in pounds) and r is the distance of the object to its center of spin (in feet). From this basic equation, the MoI for some basic shapes can be derived. Of most interest to us, however, is a simple disc, (Figure 2) which has a MoI of:
Obviously, the heavier an object of a given size, the greater its moment of inertia. But notice inertia increases with the square of the distance from the axis, meaning it is important to keep something small, as well as light, for a low MoI number. The lower the MoI, the less torque required for acceleration. You can experiment with the following: take a small object, weighing approximately a half-pound, and tie it to the end of a short string, about one foot long. Spin the object over your head-this works best if tried outside. Notice how quickly you can accelerate the rpm of the spin, and the strength required. Now, lengthen the string to a few feet and repeat (hopefully, the string stays tied and the experiment doesn't turn into a centrifugal force/linear trajectory experiment). More force is required to accelerate the spin for a longer string because the object is moving farther to complete each rotation and its arc velocity (or its equivalent linear speed) must be higher.
Enough of the physics, what about your bike? There are many ways in which rotational inertia affects the handling of a motorcycle, but the two which we will deal with are the moment of inertia of spinning parts, such as wheels and crankshafts, and the MoI of the whole motorcycle when turned into a corner. To show the importance of inertia as it pertains to rotating parts, consider your bike's front wheel/tire/disc assembly as a solid disc (Figure 3, not a great approximation, but close enough to show the significance of the concept). A front tire's radius is approximately 12 inches (half the diameter of a 17-inch wheel with a tire mounted), and the assembly weighs roughly 20 pounds, giving a MoI of 10 lb ft2. To put this into perspective, recall from last issue's dyno story ("Dyno Might!") the torque (T, in foot-pounds) required to spin an object at an angular acceleration of a (in radians per second) is:
The torque required to accelerate just the 20-pound wheel from a stop to a road speed of 100 mph in 10 seconds is 4.3 foot-pounds.