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A homogeneous disk of mass $m$ is connected at $A$ and $B$ to a fork-ended shaft of negligible mass that is supported by a bearing at $C$ The disk is free to rotate about its horizontal diameter $A B,$ and the shaft is free to rotate about a vertical axis through $C$. Initially, the disk lies in a vertical plane $\left(\theta_{0}=90^{\circ}\right)$ and the shaft has an angular velocity $\dot{\phi}_{0}=16 \mathrm{rad} / \mathrm{s}$ If the disk is slightly disturbed, determine for the ensuing motion (a) the minimum value of $\phi,(b)$ the maximum value of $\theta.$

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Physics 101 Mechanics

Chapter 18

Kinetics of Rigid Bodies in Three Dimensions

Section 3

Motion of a Gyroscope

Rotation of Rigid Bodies

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

06:08

The angular velocity of a rigid body is the rate of change of the angular displacement relative to time. In SI units, it is measured in radians per second.

07:13

A disc of mass $M$ and rad…

03:13

A uniform disc of mass $M$…

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