Chapter 12: Q.38 (page 332)
Evaluate the cross products and . (part )


Short Answer
The cross product is and into the page. (part a)
The cross product isand out of the page.(part b)
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Chapter 12: Q.38 (page 332)
Evaluate the cross products and . (part )


The cross product is and into the page. (part a)
The cross product isand out of the page.(part b)
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A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact?
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 two blocks in FIGURE CP12.86 are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.50 N m. If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?

A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in Figure P12.62. What is the maximum mass of the sign if the maximum tension in the cable without breaking is 300 N?

During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions in the core. But after all the hydrogen 鈥渇uel鈥 is consumed by nuclear fusion, the pressure force drops and the star undergoes a gravitational collapse
until it becomes a neutron star. In a neutron star, the electrons and protons of the atoms are squeezed together by gravity until they fuse into neutrons. Neutron stars spin very rapidly and emit intense pulses of radio and light waves, one pulse per rotation. These 鈥減ulsing
stars鈥 were discovered in the 1960s and are called pulsars.
a. A star with the mass M = 2.0 x 1030 kg and size R =7.0 x 108 m of our sun rotates once every 30 days. After undergoing gravitational collapse, the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.10 s. By treating the neutron star as a solid sphere, deduce its radius.
b. What is the speed of a point on the equator of the neutron star? Your answers will be somewhat too large because a star cannot be accurately modeled as a solid sphere. Even so, you will be able to show that a star, whose mass is 106larger than the earth鈥檚, can be compressed by gravitational forces to a size smaller than a typical state in the United States!
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