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The quantity \ (mr^2\) is called the rotational inertia or moment of inertia of a point mass \ (m\) a distance \ (r\) from the center of rotation. Figure \ (\PageIndex {2}\): An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies centripetal force.
Learning Objectives. By the end of this section, you will be able to: Understand the relationship between force, mass and acceleration. Study the turning effect of force. Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.
Rotational Motion. We are going to consider the motion of a rigid body about a fixed axis of rotation. The angle of rotation is measured in radians: (rads) . s. (dimensionless) r. s . Notice that for a given angle , the ratio s/r is independent of the size of the circle.
The rotational inertia of a composite object is the sum of the rotational inertias of each component, all calculated about the same axis. Itotal = I1 + I2 + I3 + …. So for a ring and a disk stacked upon each other and rotating about the symmetry axis of both, the rotational inertia is: Itotal = Iring + Idisk.
Calculating Rotational Inertia for Continuous Objects. Our task is to compute the rotational inertia, for which the formula in terms of masses and their positions is different from the one for center of mass (see Section 4.2), but the procedure is exactly the same.
We can obtain its rotational inertia I from the formula for the rotational inertia of an annular cylinder by substituting. We have. (c) Solid disk of width. *Move the Mouse over the image for an Animated View. Let R be the radius, thickness and be the density of the disk.
B )Example: Disk and String. In the last unit we developed the vector equation that determines rotational dynamics, that the net torque on a system of particles about a given axis is equal to the product of the moment of inertia of the system about that axis and the angular acceleration. t =.
