Weights of mass 5.0kg and 7.0kg are mounted 4.0m apart on a light rod, determine the moment of inertia of the system when rotated about an axis half way between the weights.
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Answer:
far in this chapter, we have been working with rotational kinematics: the description of motion for a rotating rigid body with a fixed axis of rotation. In this section, we define two new quantities that are helpful for analyzing properties of rotating objects: moment of inertia and rotational kinetic energy. With these properties defined, we will have two important tools we need for analyzing rotational dynamics.
Rotational Kinetic Energy
Any moving object has kinetic energy. We know how to calculate this for a body undergoing translational motion, but how about for a rigid body undergoing rotation? This might seem complicated because each point on the rigid body has a different velocity. However, we can make use of angular velocity—which is the same for the entire rigid body—to express the kinetic energy for a rotating object. (Figure) shows an example of a very energetic rotating body: an electric grindstone propelled by a motor. Sparks are flying, and noise and