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Referring to Prob. $18.143,(a)$ prove that the Poinsot ellipsoid is tangent to the invariable plane, ( $b$ ) show that the motion of the rigid body must be such that the Poinsot ellipsoid appears to roll on the invariable plane. (Hint: In part $a$, show that the normal to the Poinsot ellipsoid at the tip of $\omega$ is parallel to $\mathbf{H}_{o}$. It is recalled that the direction of the normal to a surface of equation $F(x, y, z)=$ constant at a point $P$ is the same as that of grad $F$ at point $P$.)

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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

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

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.

02:16

Show that the equation of …

01:53

Show that the tangent plan…

02:58

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