Essential University Physics, 3e (Wolfson)Chapter 11 Rotational Vectors and Angular Momentum

11.1 Conceptual Questions

1) If two vectors are perpendicular to each other, their cross product must be zero.A) TrueB) FalseAnswer: BVar: 1

2) If two vectors point in opposite directions, their cross product must be zero.A) TrueB) FalseAnswer: AVar: 1

3) If and are nonzero vectors for which ∙ = 0, it must follow that

A) × = 0.

B) is parallel to .

C) | × | = AB.

D) | × | = 1.

Answer: CVar: 1

4) As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?A) upB) downC) to your leftD) to your rightE) forwardsAnswer: BVar: 1

5) When you ride a bicycle, in what direction is the angular velocity of the wheels?A) to your leftB) to your rightC) forwardsD) backwardsE) upAnswer: AVar: 1

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6) The angular momentum of a system remains constantA) when the total kinetic energy is constant.B) when no net external force acts on the system.C) when the linear momentum and the energy are constant.D) when no torque acts on the system.E) all the time since it is a conserved quantity.Answer: DVar: 1

7) A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this collision

A) the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system.B) the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar.C) the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.D) both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.E) both the linear momentum and the angular momentum of the system (ball and bar) are conserved.Answer: CVar: 1

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11.2 Problems

1) What is the vector product of = 2.00 + 3.00 + 1.00 and = 1.00 - 3.00 - 2.00 ?

A) -3.00 + 5.00 - 9.00

B) -5.00 + 2.00 - 6.00

C) -9.00 - 3.00 - 3.00

D) -4.00 + 3.00 - 1.00

E) 2.00 -9.00 - 2.00 Answer: AVar: 1

2) What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?A) 6.93B) -6.93C) 4.00D) -4.00E) 8.00Answer: AVar: 1

3) If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors?Answer: 26.6°Var: 1

4) If = -4 - 2 - 3 , what is × ?

A) +3 - 4

B) +3 + 4

C) -3 + 4

D) +3 + 2 - 4

E) -3 - 2 + 4Answer: AVar: 50+

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5) If = -2 - 6 + 2 and = -2 -2 - 3 , which of the following numbers is closest to the

magnitude of × ?

A) 25B) 21C) 17D) 13E) 9Answer: AVar: 50+

6) For the vectors shown in the figure, find the magnitude and direction of × , assuming that

the quantities shown are accurate to two significant figures.

A) 26, directed into the planeB) 26, directed out of the planeC) 31, directed on the planeD) 31, directed into the planeE) 31, directed out of the planeAnswer: AVar: 1

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7) For the vectors shown in the figure, find the magnitude and direction of the vector product

× , assuming that the quantities shown are accurate to two significant figures.

A) 16, directed into the planeB) 16, directed out of the planeC) 45, directed on the planeD) 45, directed into the planeE) 45, directed out of the planeAnswer: EVar: 1

8) A force = 3.00 N - 2.00 N acts at a location = 1.00 m + 2.00 m on an object. What is

the torque that this force applies about an axis through the origin perpendicular to the xy-plane?A) -1.00 N∙m

B) 7.00 N∙m

C) -3.00 N∙m

D) 5.00 N∙m

E) -8.00 N∙m Answer: EVar: 1

9) What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force

= 5 N - 2 N + 3 N acts on the particle?

A) (8 + - 26 ) N∙m

B) (8 - 19 - 26 ) N∙m

C) (8 + 2 + ) N∙m

D) (16 - 19 - 26 ) N∙m

E) (8 - 2 + ) N∙mAnswer: BVar: 1

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10) Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. Two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system.A) 298 kg∙m2/sB) 778 kg∙m2/sC) 257 kg∙m2/sD) 222 kg∙m2/sAnswer: AVar: 50+

11) A potter's wheel, with rotational inertia is spinning freely at 40 rpm. The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay? A) 8.0 kgB) 5.4 kgC) 7.0 kgD) 8.8 kgAnswer: AVar: 38

12) A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?A) 2.0 kg∙m2/s towards the westB) 5.0 kg∙m2/s vertically upwardsC) 2.0 kg∙m2/s towards the eastD) 5.0 kg∙m2/s towards the eastE) 5.0 kg∙m2/s towards the westAnswer: AVar: 1

13) A 500-g particle is located at the point = 4m + 3m - 2m and is moving with a velocity

= 5 m/s -2 ms + 4 m/s . What is the angular momentum of this particle about the origin?

A) (24 - 6 - 8 ) kg∙m2/s

B) (12 - 3 - 4 ) kg∙m2/s

C) (8 + 14 - 13 ) kg∙m2/s

D) (10 - + 2 ) kg∙m2/s

E) (4 - 13 - 11.5 ) kg∙m2/sAnswer: EVar: 1

14) A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25

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kg∙m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg∙m2, what is the final angular speed?A) 2.25 rad/sB) 4.60 rad/sC) 6.25 rad/sD) 1.76 rad/sE) 0.810 rad/sAnswer: CVar: 1

15) A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg∙m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. What is the angular speed of the merry-go-round right after the two people have stepped on?A) 0.20 rad/sB) 0.40 rad/sC) 0.60 rad/sD) 0.80 rad/sE) 0.67 rad/sAnswer: BVar: 1

16) A record is dropped vertically onto a freely rotating (undriven) turntable. Frictional forces act to bring the record and turntable to a common angular speed. If the rotational inertia of the record is 0.54 times that of the turntable, what percentage of the initial kinetic energy is lost?A) 35%B) 18%C) 46%D) 60%Answer: AVar: 50+

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17) A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure). What is the angular velocity of the turntable just after the ball is caught?

A) 2.1 rad/sB) 1.3 rad/sC) 0.94 rad/sD) 0.75 rad/sE) 0.30 rad/sAnswer: BVar: 1

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18) A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure). The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to

A) 45%.B) 51%.C) 55%.D) 60%.E) 65%.Answer: BVar: 1

19) A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system?A) 0.93 /s

B) 1.1 /s

C) 1.3 /s

D) 1.6 /s

E) 1.9 /sAnswer: AVar: 50+

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20) An object is rotating with an angular momentum 4.00 kg∙m2/s while being acted on by a

constant torque 3.00 N∙m . What is the angular speed of precession of the angular velocity of the object?A) 1.33 rad/sB) 0.750 rad/sC) 12.0 rad/sD) zeroE) It depends on the moment of inertia of the object.Answer: BVar: 1

21) In the figure, the rotor of a gyroscope is a uniform disk that has a radius of 13.8 cm and a moment of inertia about its axis of 4.0 × 10-3 kg∙m2. The length of the rotor shaft is 6.9 cm. The ball pivot at P is frictionless. At a given instant, the rotor shaft is horizontal and the rotor is rotating with an angular velocity of 90 rad/s about its axis OP, as shown. The rotor is viewed from point Q on the axis. The precessional linear velocity of point O, including the direction seen from point Q, is closest to

A) 0.054 m/s, leftwardB) 0.054 m/s, upwardC) 0.054 m/s, rightwardD) 0.11 m/s, downwardE) 0.11 m/s, rightwardAnswer: AVar: 1

22) 61)A bicycle wheel of radius 0.36 m and mass 3.2 kg is set spinning at 4.00 rev/s. A very light bolt is attached to extend the axle in length, and a string is attached to the axle at a distance of 0.10 m from the wheel. Initially the axle of the spinning wheel is horizontal, and the wheel is suspended only from the string. We can ignore the mass of the axle and spokes. At what rate will the wheel process about the vertical?A) 2.9 rpmB) 1.9 rpmC) 18 rpmD) 0.30 rpmE) 0.77 rpmAnswer: AVar: 1

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