91影视

Question: (III) An asteroid of mass \({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{\bf{5}}}\;{\bf{kg}}\) traveling at a speed of \({\bf{35}}\;{{{\bf{km}}} \mathord{\left/{\vphantom {{{\bf{km}}} {\bf{s}}}} \right.} {\bf{s}}}\) relative to the Earth, hits the Earth at the equator tangentially, in the direction of Earth鈥檚 rotation, and is embedded there. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.

A merry-go-round with a moment of inertia equal to \({\bf{1260}}\;{\bf{kg}} \cdot {{\bf{m}}{\bf{2}}}\) and a radius of 2.5 m rotates with negligible friction at \({\bf{1}}{\bf{.70}}\;{{{\bf{rad}}} \mathord{\left/ {\vphantom {{{\bf{rad}}} {\bf{s}}}} \right. \\{\bf{s}}}\). A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to \({\bf{1}}{\bf{.35}}\;{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.

\\{\bf{s}}}\). What is her mass?

On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius \({{\bf{R}}_{\bf{1}}}{\bf{ = 2}}{\bf{.5}}\;{\bf{cm}}\) and winds its way out to radius \({{\bf{R}}_{\bf{2}}}{\bf{ = 5}}{\bf{.8}}\;{\bf{cm}}\). To read the digital information, a CD player rotates the CD so that the player鈥檚 readout laser scans along the spiral鈥檚 sequence of bits at a constant linear speed of 1.25 m/s. Thus the player must accurately adjust the rotational frequency f of the CD as the laser moves outward. Determine the values for f (in units of rpm) when the laser is located at \({{\bf{R}}_{\bf{1}}}\) and when it is at \({{\bf{R}}_{\bf{2}}}\).

(a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.013 m. Use conservation of energy to calculate the linear speed of the yo-yo just before it reaches the end of its 1.0-m-long string, if it is released from rest. (b) What fraction of its kinetic energy is rotational?

A cyclist accelerates from rest at a rate of \({\bf{1}}{\bf{.00}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How fast will a point at the top of the rim of the tire (diameter = 0.80 cm) be moving after 2.25 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest 鈥� sees Fig. 8鈥�57.]

FIGURE 8-57 Problem 79

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

A hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.0 m/s when it reaches a 15掳 incline. (a) How far up the incline will it go? (b) How long will it be on the incline before it arrives back at the bottom?

Determine the angular momentum of the Earth (a) about its rotation axis (assume the Earth is a uniform sphere), and (b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun).

A wheel of mass M has radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8鈥�60). The step has height h, where h < R. What minimum force F is needed?

If the coefficient of static friction between a car鈥檚 tires and the pavement is 0.65, calculate the minimum torque that must be applied to the 66-cm-diameter tire of a 1080-kg automobile in order to 鈥渓ay rubber鈥� (make the wheels spin, slipping as the car accelerates). Assume each wheel supports an equal share of the weight.