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#37. A small blob of putty of mass m falls from the ceiling and lands on the outer rim of a
turntable of radius R and moment of intertia Io that is rotating freely with angular speed
ωi about its vertical fixed symmetry axis. (a) What is the postcollision angular speed of
the turntable plus putty? (b) After several turns, the blob flies off the edge of the
turntable. What is the angular speed of the turntable after the blob flies off?

40. At the beginning of each term, a physics professor named Dr. Zeus shows the class
his expectations of them through a demonstration that he calls “Lesson #1.” He stands at
the center of a turntable that can rotate without friction. He then takes a 2 kg globe of the
earth and swings it around his head at the end of a 0.8 m chain. The world revolves
around him every 3 seconds, and the professor and the platform have a moment of inertia
of 0.5 kg m2. (a) What is the angular speed of the professor? -5.36 rad/s(b) What is the
total kinetic energy of the globe, professor, and platform? 10 J

66. An object of mass M is rotating about a fixed axis with angular momentum L. Its
moment of inertia about this axis is I. What is its kinetic energy? b
       a. IL2/2
       b. L2/2I
       c. ML2/2
       d. IL2/2M

Optional Problems

Pg. 253

105. A 4-kg fish is swimming at 1.5 m/s to the right. He swallows a 1.2-kg fish
swimming towards him at 3 m/s. Neglecting water resistance, what is the velocity of the
larger fish immediately after his lunch?

111. A 60-kg woman stands on the back of a 6-m-long, 120-kg raft that is floating at rest
in still water with no friction. The raft is 0.5 m from a fixed pier, as in Figure 8-58.
         (a) The woman walks to the front of the raft and stops. How far is the raft from
             the pier now?
         (b) While the woman walks, she maintains a constant speed of 3 m/s relative to
             the raft. Find the total kinetic energy of the system (woman plus raft), and
             compare with the kinetic energy if the woman walked at 3 m/s on a raft tied to
             the pier.
         (c) Where does this energy come from, and where does it go when the woman
             stops at the front of the raft?
         (d) On land, the woman can put a lead shot 6 m. She stands at the back of the raft,
             aims forward, and puts the shot so that just after it leaves her hand, it has the
             same velocity relative to her as it does when she throws it from the ground.
             Where does the shot land?
Pg. 313

15. A 2-kg particle moves at a constant speed of 3.5 m/s around a circle of radius 4 m. (a)
What is its angular momentum about the center of the circle? (b) What is its momentum
of inertia about an axis through the center of the circle and perpendicular to the plane of
the motion? (c) What is the angular speed of the particle?

29. If the angular momentum of a system is constant, which of the following statements
must be true?
         (a) No torque acts on any part of the system.
         (b) A constant torque acts on each part of the system.
         (c) Zero net torque acts on each part of the system.
         (d) A constant external torque acts on the system.
         (e) Zero net torque acts on the system.

33. A block sliding on a frictionless table is attached to a string that passes through a hole
in the table. Initially, the block is sliding with speed vo in a circle of radius ro. A student
under the table pulls slowly on the string. What happens as the block spirals inward?
Give supporting arguments for your choice.
         (a) Its energy and angular momentum are conserved.
         (b) Its angular momentum is conserved, and its energy increases.
         (c) Its angular momentum is conserved, and its energy decreases.
         (d) Its energy is conserved, and its angular momentum increases.
         (e) Its energy is conserved, and its angular momentum decreases.

35. Under gravitational collapse (all forces on various pieces are inward toward the
center), the radius of a spinning spherical star of uniform density shrinks by a factor of 2,
with the resulting increased density remaining uniform throughout as the star shrinks.
What will be the ratio of the final angular speed ω2 to the initial angular speed ω1?
(a) 2                                  (b) 0.5                                (c) 4
(d) 0.25                               (e) 1.0

								
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