Rotational Kinetic EnergyĪny moving object has kinetic energy. With these properties defined, we will have two important tools we need for analyzing rotational dynamics. In this section, we define two new quantities that are helpful for analyzing properties of rotating objects: moment of inertia and rotational kinetic energy. So 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. Calculate the angular velocity of a rotating system when there are energy losses due to nonconservative forces.Use conservation of mechanical energy to analyze systems undergoing both rotation and translation.Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy.Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis.Describe the differences between rotational and translational kinetic energy.The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis.By the end of this section, you will be able to: The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics-both characterize the resistance of a body to changes in its motion. m 2) in SI units and pound-foot-second squared (lbf.Moments of inertia may be expressed in units of kilogram metre squared (kg The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. When a body is free to rotate around an axis, torque must be applied to change its angular momentum. In mechanical engineering, simply "inertia" is often used to refer to " inertial mass" or " moment of inertia". For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3-by-3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other. Its simplest definition is the second moment of mass with respect to distance from an axis.įor bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters.
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The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation by a given amount. The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.
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To improve their maneuverability, combat aircraft are designed to minimize moments of inertia, while civil aircraft often are not.