(II) A toy gyroscope consists of a 170-g disk with a radius of 5.5 cm mounted at the center of a thin axle 21 cm long (Fig. 11–41). The gyroscope spins at 45 rev/s. One end of its axle rests on a stand and the other end precesses horizontally about the stand. ( a ) How long does it take the gyroscope to precess once around? ( b ) If all the dimensions of the gyroscope were doubled (radius = 11 cm. axle = 42 cm), how long would it take to precess once? FIGURE 11–41 A wheel, rotating about a horizontal axle supported at one end, precesses. Problems 54, 55, and 56.
(II) A toy gyroscope consists of a 170-g disk with a radius of 5.5 cm mounted at the center of a thin axle 21 cm long (Fig. 11–41). The gyroscope spins at 45 rev/s. One end of its axle rests on a stand and the other end precesses horizontally about the stand. ( a ) How long does it take the gyroscope to precess once around? ( b ) If all the dimensions of the gyroscope were doubled (radius = 11 cm. axle = 42 cm), how long would it take to precess once? FIGURE 11–41 A wheel, rotating about a horizontal axle supported at one end, precesses. Problems 54, 55, and 56.
(II) A toy gyroscope consists of a 170-g disk with a radius of 5.5 cm mounted at the center of a thin axle 21 cm long (Fig. 11–41). The gyroscope spins at 45 rev/s. One end of its axle rests on a stand and the other end precesses horizontally about the stand. (a) How long does it take the gyroscope to precess once around? (b) If all the dimensions of the gyroscope were doubled (radius = 11 cm. axle = 42 cm), how long would it take to precess once?
FIGURE 11–41 A wheel, rotating about a horizontal axle supported at one end, precesses. Problems 54, 55, and 56.
(II) A small rubber wheel is used to drive a large potterywheel. The two wheels are mounted so that their circularedges touch. The small wheel has a radius of 2.0 cm andaccelerates at the rate of 7.2 rad/s and it is in contact withthe pottery wheel (radius 27.0 cm) without slipping. Calculate
(a) the angular acceleration of the pottery wheel, and(b) the time it takes the pottery wheel to reach its requiredspeed of 65 rpm
(II) A ball of mass M and radius r on the end of a thin
massless rod is rotated in a horizontal circle of radius Ro
about an axis of rotation AB, as shown in Fig. 10-58.
(a) Considering the mass of the ball to be concentrated at
its center of mass, calculate its moment of inertia about AB.
(b) Using the parallel-axis theorem and considering the
finite radius of the ball, calculate the moment of inertia of
the ball about AB. (c) Calculate the percentage error intro-
duced by the point mass approximation for r
1.0 m. s
9.0 cm and
%3D
Ro
to Toinso odt 1s oizs IsB
gadsion ai m
%3D
08.2
(E 10-0
boT
Ro
UKE or da
Problem 89.
► M
10-65
FIGURE 10-58
molecule. The
H bonds
incrtia
Problem 58.
A
gl00A
(I) A 52-kg person riding a bike puts all her weight on eachpedal when climbing a hill. The pedals rotate in a circle ofradius 17 cm. (a) What is the maximum torque she exerts?(b) How could she exert more torque?
Chapter 11 Solutions
Physics for Scientists and Engineers with Modern Physics
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