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Chapter 11: Problem 1
Does Earth's angular velocity vector point north or south?
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If you increase the rotation rate of a precessing gyroscope, will the precession rate increase or decrease?
A particle of mass \(m\) moves in a straight line at constant speed v. Show that its angular momentum about a point located a perpendicular distance \(b\) from its line of motion is \(m v b\) regardless of where the particle is on the line.
A tumtable of radius \(15 \mathrm{~cm}\) and rotational inertia \(0.0115 \mathrm{~kg} \cdot \mathrm{m}^{2}\) is spinning freely at \(32.0 \mathrm{rpm}\) about its central axis, with a \(20.5-\mathrm{g}\) mouse on its outer edge. The mouse walks from the edge to the center. Find (a) the new rotation speed and (b) the work done by the mouse.
Jumbo is back! Jumbo is the 4.8-Mg elephant from Example 9.4. This time he's standing at the outer edge of a \(15-\mathrm{Mg}\) turntable of radius \(8.5 \mathrm{~m}\), rotating with angular velocity \(0.15 \mathrm{~s}^{-1}\) on frictionless bearings. Jumbo then walks to the center of the turntable. Treating Jumbo as a point mass and the turntable as a solid disk, find (a) the angular velocity of the turntable once Jumbo reaches the center and (b) the work Jumbo does in walking to the center.
When a star like our Sun exhausts its fuel, thermonuclear reactions in its core cease, and it collapses to become a white dwarf. Often the star will blow off its outer layers and lose some mass before it collapses. Suppose a star with the Sun's mass and radius is rotating with period 25 days and then collapses to a white dwarf with \(55 \%\) of the Sun's mass and a rotation period of \(131 \mathrm{~s}\). What's the radius of the white dwarf? Compare your answer with the radii of Earth and the Sun.
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