Calculating the Rotational Inertia

Calculating the Rotational Inertia If a rigid body consists of a few particles. we can calculate its rotational inertia about a given rotation axis with  that is we can find the product for each particle and then sum the products. Gives the results of such integration for nine coinmon body shapes and the indicated axes of rotation.

Sample Problem

Sample Problem Shows a centrifuge used to accustom astronaut trainees to high accelerations. The radius r of the circle traveled by an astronaut. (a) At what constant angular speed must the centrifuge rotate if the astronaut is to have a linear acceleration of magnitude. SOLUTION: The Key Idea is this.Because the angular speed is constant, the angular acceleration. (b) …

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The Speed

The Speed However, is the linear speed (the magnitude of the linear velocity) of the point in question,  is the angular speed ta of the rotating body. Caution: The angular speed w must be expressed in radian measure. Equation 11-18 tells us’ that since all points within the rigid body have the same angular speed w, points …

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The Position

The Position If a reference line on a rigid body rotates through an angle 0, a point within the body at a position r from the rotation axis moves a distance s along a circular. This is the first of our linear-angular relations. Caution: The angle 0 here must be measured in radians because is itself the …

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