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PHYS 361 Homework due Friday, November 5 15 Points 1. A gyroscope similar to the one shown in Symon, Figure 4.1, has mass M and a moment of inertia about its own symmetry axis I. The center of mass of the wheel lies along the perpendicular axis, a distance ℓ from the pivot point Q. The gyroscope rotates rapidly about its own symmetry axis with an angular velocity ω, creating an angular momentum vector perpendicular to the wheel that tends to be conserved. The angular momentum of the wheel is however, subject to a torque from gravity. The torque due to gravity causes the precession about the vertical direction depicted in Figure 4.1. Show that the angular velocity of precession is ωp = Mgl . Iω 2. A projectile of mass M breaks into two fragments in mid-air at an instant that its v altitude was 350 m and its velocity was v = 120 m/s xˆ + 23 m/s yˆ , where y is the vertical direction and x is horizontal. The smaller fragment, 0.3M, is ejected straight down at − 50 m/s ŷ relative to the center of mass. How long does it take the larger fragment to reach the ground? 3. Symon, Chapter 4, Problem 2.