PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HOMEWORK PROBLEMS Chapter 8:
ROTATIONAL EQUILIBRIUM AND
ROTATIONAL DYNAMICS
HW-8
PART-A: Hand in your answers in class on scantron on Monday 08 November-2010. Write
your name, class (1401) and HW # 8 on the scantron.
1. A wrench 0.500 m long is applied to a nut with a force of 80.0 N. Because of the cramped
space, the force must be exerted upward at an angle of 60.0° with respect to a line from the bolt
through the end of the wrench. How much torque is applied to the nut? (a) 34.6 N · m (b) 4.56
N · m (c) 11.8 N · m (d) 14.2 N · m (e) 20.0 N · m
2. A horizontal plank 4.00 m long and having mass 20.0 kg rests on two pivots, one at the left
end and a second 1.00 m from the right end. Find the magnitude of the force exerted on the
plank by the second pivot. (a) 32.0 N (b) 45.2 N (c) 112 N (d) 131 N (e) 98.2 N
3. What is the magnitude of the angular acceleration of a 25.0-kg disk of radius 0.800 m when a
torque of magnitude 40.0 N · m is applied to it? (a) 2.50 rad/s2 (b) 5.00 rad/s2 (c) 7.50 rad/s2 (d)
10.0 rad/s2 (e) 12.5 rad/s2
4. Estimate the rotational kinetic energy of Earth by treating it as a solid sphere with uniform
density. (a) 3 X 1029 kg · m2/s2 (b) 5 X 1027 kg · m2/s2 (c) 7 X 1030 kg · m2/s2 (d) 4 X 1028 kg ·
m2/s2 (e) 2 X 1025 kg · m2/s2
5. Two forces are acting on an object. Which of the following statements is correct? (a) The
object is in equilibrium if the forces are equal in magnitude and opposite in direction. (b) The
object is in equilibrium if the net torque on the object is zero. (c) The object is in equilibrium if
the forces act at the same point on the object. (d) The object is in equilibrium if the net force
and the net torque on the object are both zero. (e) The object cannot be in equilibrium because
more than one force acts on it.
6. A disk rotates about a fixed axis that is perpendicular to the disk and passes through its
center. At any instant, does every point on the disk have the same (a) centripetal acceleration,
(b) angular velocity, (c) tangential acceleration, (d) linear velocity, or (e) total acceleration?
7- BLANK
8. A block slides down a frictionless ramp, while a hollow sphere and a solid ball roll without
slipping down a second ramp with the same height and slope. Rank the arrival times at the
bottom from shortest to longest. (a) sphere, ball, block (b) ball, block, sphere (c) ball, sphere,
block (d) block, sphere, ball (e) block, ball, sphere
9. A solid disk and a hoop are simultaneously released from rest at the top of an incline and roll
down without slipping. Which object reaches the bottom first? (a) The one that has the largest
mass arrives first. (b) The one that has the largest radius arrives first. (c) The hoop arrives first.
(d) The disk arrives first. (e) The hoop and the disk arrive at the same time.
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PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-8
10. A solid cylinder of mass M and radius R rolls down an incline without slipping. Its moment
of inertia about an axis through its center of mass is MR2/2. At any instant while in motion, its
rotational kinetic energy about its center of mass is what fraction of its total kinetic energy? (a)
12 (b) 14 (c) 13 (d) 25 (e) None of these
11. The cars in a soapbox derby have no engines; they simply coast downhill. Which of the
following design criteria is best from a competitive point of view? The car’s wheels should (a)
have large moments of inertia, (b) be massive, (c) be hoop-like wheels rather than solid disks,
(d) be large wheels rather than small wheels, or (e) have small moments of inertia.
12. Consider two uniform, solid spheres, a large, massive sphere and a smaller, lighter sphere.
They are released from rest simultaneously from the top of a hill and roll down without
slipping. Which one reaches the bottom of the hill first? (a) The large sphere reaches the
bottom first. (b) The small sphere reaches the bottom first. (c) The sphere with the greatest
density reaches the bottom first. (d) The spheres reach the bottom at the same time. (e) The
answer depends on the values of the spheres’ masses and radii.
13. A mouse is initially at rest on a horizontal turntable mounted on a frictionless, vertical axle.
As the mouse begins to walk clockwise around the perimeter, which of the following
statements must be true of the turntable? (a) It also turns clockwise. (b) It turns
counterclockwise with the same angular velocity as the mouse. (c) It remains stationary. (d) It
turns counterclockwise because angular momentum is conserved. (e) It turns counterclockwise
because mechanical energy is conserved.
14. According to the manual of a certain car, a maximum torque of magnitude 65.0 N · m
should be applied when tightening the lug nuts on the vehicle. If you use a wrench of length
0.330 m and you apply the force at the end of the wrench at an angle of 75.0° with respect to a
line going from the lug nut through the end of the handle, what is the magnitude of the
maximum force you can exert on the handle without exceeding the recommendation?
(a) 122 N
(b) 184 N
(c) 204 N
(d) 254 N
15. A student gets his car stuck in a snowdrift. Not at a loss, having studied physics, he attaches
one end of a stout rope to the car and the other end to the trunk of a nearby tree, allowing for a
small amount of slack. The student then exerts a force on the center of the rope in the
direction perpendicular to the car-tree line as shown in Figure P8.25. If the rope is inextensible
and the magnitude of the applied force is 475 N, what is the force on the car? (Assume
equilibrium conditions.)
(a) 2.56 kN
(b) 2.86 kN
(c) 3.04 kN
2
(d) 4.04 kN
PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-8
PART-B: Hand in your solutions to the following questions in class, on Monday 08 November2010. Box your final answers clearly
A uniform beam of length 7.60 m and weight 4.50 X 102 N is carried by two workers,
Sam and Joe, as shown in Figure P8.8. (a) Determine the forces that each person exerts on
the beam. (b) Qualitatively, how would the answers change if Sam moved closer to the
midpoint? (c) What would happen if Sam moved beyond the midpoint
8.
22. A hungry 700-N bear walks out on a beam in an attempt to retrieve some “goodies”
hanging at the end (Fig. P8.22). The beam is uniform, weighs 200 N, and is 6.00 m long;
the goodies weigh 80.0 N. (a) Draw a free-body diagram of the beam. (b) When the bear is
at x = 1.00 m, find the tension in the wire and the components of the reaction force at the
hinge. (c) If the wire can withstand a maximum tension of 900 N, what is the maximum
distance the bear can walk before the wire breaks?
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PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-8
31. Four objects are held in position at the corners of a rectangle by light rods as shown in
Figure P8.31. Find the moment of inertia of the system about (a) the x-axis, (b) the y-axis,
and (c) an axis through O and perpendicular to the page.
40.
An Atwood’s machine consists of blocks of masses m1 = 10.0 kg and m2 = 20.0 kg
attached by a cord running over a pulley as in Figure P8.40. The pulley is a solid cylinder
with mass M = 8.00 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop,
and the cord turns the pulley without slipping. (a) Why must the tension T2 be greater than
the tension T1? (b) What is the acceleration of the system, assuming the pulley axis is
frictionless? (c) Find the tensions T1 and T2.
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PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-8
52. Use conservation of energy to determine the angular speed of the spool shown in Figure
P8.52 after the 3.00-kg bucket has fallen 4.00 m, starting from rest. The light string attached
to the bucket is wrapped around the spool and does not slip as it unwinds.
58. Halley’s comet moves about the Sun in an elliptical orbit, with its closest approach to the
Sun being 0.59 A.U. and its greatest distance being 35 A.U. (1 A.U. is the Earth– Sun
distance). If the comet’s speed at closest approach is 54 km/s, what is its speed when it is
farthest from the Sun? You may neglect any change in the comet’s mass and assume that its
angular momentum about the Sun is conserved.
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PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-8
60. A playground merry-go-round of radius 2.00 m has a moment of inertia I = 275 kg · m2
and is rotating about a frictionless vertical axle. As a child of mass 25.0 kg stands at a
distance of 1.00 m from the axle, the system (merry-go-round and child) rotates at the rate
of 14.0 rev/min. The child then proceeds to walk toward the edge of the merry-go-round.
What is the angular speed of the system when the child reaches the edge?
87. A 4.00-kg mass is connected by a light cord to a 3.00-kg mass on a smooth surface (Fig.
P8.87). The pulley rotates about a frictionless axle and has a moment of inertia of 0.500 kg
· m2 and a radius of 0.300 m. Assuming that the cord does not slip on the pulley, find (a)
the acceleration of the two masses and (b) the tensions T1 and T2.
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