# 10.4 Moment of Inertia and Rotational Kinetic Energy – University Physics Volume 1.pdf

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2/15/202110.4 Moment of Inertia and Rotational Kinetic Energy – University Physics Volume 11/2210 Fixed-Axis Rotation10.4 Moment of Inertia and RotationalKinetic EnergyLearning ObjectivesBy the end of this section, you will be able to:Describe the differences between rotational and translational kinetic energyDefine the physical concept of moment of inertia in terms of the mass distributionfrom the rotational axis
2/15/202110.4 Moment of Inertia and Rotational Kinetic Energy – University Physics Volume 12/22Explain how the moment of inertia of rigid bodies affects their rotational kineticenergyUse conservation of mechanical energy to analyze systems undergoing both rotationand translationCalculate the angular velocity of a rotating system when there are energy losses due tononconservative forcesSo far in this chapter, we have been working with rotational kinematics: the description of motionfor a rotating rigid body with a fixed axis of rotation. In this section, we define two new quantitiesthat are helpful for analyzing properties of rotating objects: moment of inertia and rotational ki‐netic energy. With these properties defined, we will have two important tools we need for analyz‐ing rotational dynamics.Rotational Kinetic EnergyAny moving object has kinetic energy. We know how to calculate this for a body undergoingtranslational motion, but how about for a rigid body undergoing rotation? This might seem com‐plicated because each point on the rigid body has a different velocity. However, we can make useof angular velocity—which is the same for the entire rigid body—to express the kinetic energy fora rotating object.(Figure)shows an example of a very energetic rotating body: an electric grind‐stone propelled by a motor. Sparks are flying, and noise and vibration are generated as the grind‐stone does its work. This system has considerable energy, some of it in the form of heat, light,sound, and vibration. However, most of this energy is in the form ofrotational kinetic energy.
2/15/202110.4 Moment of Inertia and Rotational Kinetic Energy – University Physics Volume 13/22Figure 10.17The rotational kinetic energy of the grindstone is converted to heat, light, sound, andvibration. (credit: Zachary David Bell, US Navy)Energy in rotational motion is not a new form of energy; rather, it is the energy associated withrotational motion, the same as kinetic energy in translational motion. However, because kineticenergy is given by, and velocity is a quantity that is different for every point on a rotating body about an axis, itmakes sense to find a way to write kinetic energy in terms of the variable

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