Download University Physics-1 Ch-10 NAME: HOMEWORK CHAPTER 10

University Physics-1
Ch-10
NAME: _____________________________________________
HOMEWORK CHAPTER 10:
ROTATION OF A RIGID BODY ABOUT A FIXED AXIS
NOTE:
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Hand in your solutions in class in the lecture period after which the chapter is completed.
2
Show the equations and calculations, and box your answer. Be sure to include the units.
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You are required to solve all problems. Instructor will select and grade any four questions, and
the marks for this HW will be based on these only.
1.
During a certain period of time, the angular position of a swinging door is described by:
θ = 5.00 + 18.0t + 2.50t2, where θ is in radians and t is in seconds. Determine the angular position,
velocity and acceleration of the door at t = 2.00 s.
2
A wheel starts from rest and rotates with constant angular acceleration to reach an
angular speed of 16.0 rad/s in 3.60 s. Find the angle through which it rotates in this time and the
angular acceleration.
3.
A centrifuge in a medical laboratory rotates at an angular speed of 3,000 rpm. When
switched off, it rotates through 230.0 revolutions before coming to rest. Assume that the angular
acceleration is constant and find the angular velocity after it has made 115 revolutions.
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University Physics-1
Ch-10
4
A disk 8.00 cm in radius rotates at a constant rate of 1,700 rpm about its central axis.
Determine the tangential speed, radial and tangential accelerations at a point 5.00 cm from its
center.
5
The four particles in Figure P10.21 are connected by rigid rods of negligible mass. The origin
is at the center of the rectangle. The system rotates in the yz plane about the x axis with an
angular speed of 7.00 rad/s. Calculate (a) the moment of inertia of the system about the x axis
and (b) the rotational kinetic energy of the system.
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Figure P10.27 shows a side view of a car tire. Model it as having two sidewalls of uniform
thickness 0.7 cm and a tread wall of uniform thickness 2.00 cm and width 25.0 cm. Assume the
rubber has uniform density equal to 1.20  103 kg/m3. Find its moment of inertia about an axis
through its center (hint: add the moments of inertia of the two sidewalls and the thread wall)
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7.
The fishing pole in Figure P10.32 makes an angle of 20.0° with the horizontal. What is the
torque exerted by the fish about an axis perpendicular to the page and passing through the
angler’s hand?
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Find the net torque on the wheel in Figure P10.33 about the axle through O, taking a = 15.0
cm and b = 30.0 cm.
10.0 N
9.
A grinding wheel is in the form of a uniform solid disk of radius 12.00 cm and mass 2.50 kg. It
starts from rest and accelerates uniformly under the action of the constant torque of 0.700 Nm
that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating
speed of 1,200 rev/min? By how many revolutions has it turned in this time?
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University Physics-1
Ch-10
10.
A cylinder of mass 7.0 kg rolls without slipping on a horizontal surface. At a certain instant
its center of mass has a speed of 6.0 m/s. Determine its translational, rotational and total kinetic
energy.
11.
A block of mass m1 = 2.50 kg and a block of mass m2 = 5.00 kg are connected by a
massless string over a pulley in the shape of a solid disk having radius R = 0.30 m and mass M = 7.0
kg. These blocks are allowed to move on a fixed wedge of angle θ = 40.0° as shown in Figure
P10.37. The coefficient of kinetic friction is 0.20 for both blocks. Draw free-body diagrams of both
blocks and of the pulley. Determine (a) the acceleration of the two blocks and (b) the tensions in
the string on both sides of the pulley.
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12.
A large clock tower clock has an hour hand 2.40 m long with a mass of 50.0 kg and a
minute hand 4.00 m long with a mass of 80 kg. Calculate the total rotational kinetic energy of the
two hands about the axis of rotation. (You may model the hands as long, thin rods.)
13.
Consider the system shown in Figure P10.44 with m1 = 15.0 kg, m2 = 10.0 kg, R = 0.250 m,
and the mass of the uniform pulley M = 4.00 kg. Object m2 is resting on the floor, and object m1 is
3.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light,
does not stretch, and does not slip on the pulley. Calculate the time interval required for m1 to hit
the floor. How would your answer change if the pulley were massless?
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14.
A horizontal 1000-N merry-go-round is a solid disk of radius 1.80 m, started from rest by a
constant horizontal force of 60.0 N applied tangentially to the edge of the disk. Find the kinetic
energy of the disk after 5.00 s.
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