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Chapter 12: Q. 11 (page 330)
The three 200g masses in FIGURE rigid rods.
a. What is the triangle's moment of inertia about the axis through the
b. What is the triangle's kinetic energy if it rotates about the axis
a. The moment of inertia of the triangle is
b. The rotational kinetic energy is
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An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass?
Hint: Divide the triangle into vertical strips of width dx, then relate the mass dm of a strip at position x to the values of x and dx.
A thin, uniform rod of length L and mass M is placed vertically on a horizontal table. If tilted ever so slightly, the rod will fall over.
a. What is the speed of the center of mass just as the rod hits the table if there鈥檚 so much friction that the bottom tip of the rod does not slide?
b. What is the speed of the center of mass just as the rod hits the table if the table is frictionless?
The earth鈥檚 rotation axis, which is tilted 23.5颅 from the plane of the earth鈥檚 orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earth鈥檚 rotation axis traces out a 23.5颅 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge, which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written 惟=饾湉/蝇. Although we derived this equation for a specific situation, it鈥檚 a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?
A 12-cm-diameter CD has a mass of 21g. What is the CD's moment of inertia for rotation about a perpendicular axis (a) through its center and (b) through the edge of the disk?
The 20-cm-diameter disk in FIGURE EX12.20 can rotate on an axle through its center. What is the net torque about the axle?
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