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Chapter 8: 8-13MCQ (page 198)
Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, your angular velocity will
(a) increase.
(b) decrease.
(c) stay the same.
The correct option is (c).
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An oxygen molecule consists of two oxygen atoms whose total mass is \({\bf{5}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 26}}}}\;{\bf{kg}}\) and the moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is \({\bf{1}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 46}}}}\;{\bf{kg}} \cdot {{\bf{m}}^{\bf{2}}}\). From these data, estimate the effective distance between the atoms.
Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, as shown in Fig. 8鈥�46. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate (a) the angular acceleration of the arm and (b) the force required for the triceps muscle. Assume that the forearm has a mass of 3.7 kg, and it rotates like a uniform rod about an axis at its end.
FIGURE 8-46
Problems 35 and 36
A dad pushes a small hand-driven merry-go-round tangentially and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume that the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edges. Calculate the torque required to produce the acceleration, neglecting the frictional torque. What force is required at the edge?
The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). (a) What is the angular velocity \(\left( {{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.} {\bf{s}}}} \right)\) of the platter? (b) If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it? (c) If a single bit requires \({\bf{0}}{\bf{.50}}\;{\bf{\mu m}}\) of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?
Figure 8鈥�59 illustrates an \({{\bf{H}}_{\bf{2}}}{\bf{O}}\) molecule. The \({\bf{O - H}}\) bond length is 0.096 nm and the \({\bf{H - O - H}}\) bonds make an angle of 104掳. Calculate the moment of inertia of the \({{\bf{H}}_{\bf{2}}}{\bf{O}}\)molecule (assume the atoms are points) about an axis passing through the center of the oxygen atom (a) perpendicular to the plane of the molecule, and (b) in the plane of the molecule, bisecting the \({\bf{H - O - H}}\) bonds.
FIGURE 8-59 Problem 82
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