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.