That’s where the torsional pendulum comes in - a device that measures a wheel’s rotational inertia.Įver since I built this torsional pendulum for bicycle wheels and tested the moment of inertia of some wheels in the Jissue of VeloNews, I’ve wanted to provide readers with a full explanation of the physics involved. We can measure the mass of the wheel easily enough, but it is not necessarily the case that the lightest wheel will have the lowest moment of inertia, or vice versa. Rotational inertia, or moment of inertia, is the rotational equivalent of mass this is the quantity that we want to measure to see how much energy it takes to accelerate a wheel. In the case of a wheel, it is probably obvious that it will take more work to accelerate it if the mass is concentrated out at its edge than at its center. This is not true if you drive the object by rotating it then, how the mass is distributed plays an important role in how much energy it takes to move it. If you move a rigid object in a straight line, it does not matter how its mass is distributed the amount of work to move it will be the same. You’ll need them both as Lennard busts out the physics. Grab a cup of coffee and your thinking cap. 18, 2008 issue of VeloNews (and later in the September 2010 issue). The simple analogy is that of a rod.Editor’s note: The following is an explanation of the inertia test used in the Aug. This is because the axis of rotation is closer to the center of mass of the system in (b). We see that the moment of inertia is greater in (a) than (b). Using the parallel-axis theorem eases the computation of the moment of inertia of compound objects. Refer to (Figure) for the moments of inertia for the individual objects. In both cases, the moment of inertia of the rod is about an axis at one end.

In (b), the center of mass of the sphere is located a distance R from the axis of rotation.

In (a), the center of mass of the sphere is located at a distanceįrom the axis of rotation. Since we have a compound object in both cases, we can use the parallel-axis theorem to find the moment of inertia about each axis. The radius of the sphere is 20.0 cm and has mass 1.0 kg. The rod has length 0.5 m and mass 2.0 kg. Find the moment of inertia of the rod and solid sphere combination about the two axes as shown below.

Bending moment of inertia of a circle