Homework
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HE3 2023 Fall (Optional)
The next four questions pertain to the situation described below.
Two coaxial solid disks are glued together and placed on a common axle
passing through the center of mass of the disks normal to their circular
cross sections. A constant 80 N force F is applied at the rim of the larger
disk by a string wound around its rim (the string is not shown in the
figure). The string does not slip. The radii of the smaller and larger disks,
and are 0.6 m and 0.8 meter, respectively, but the disks have
identical masses M
. The disks are initially at rest. At t = 0 the disks are
allowed to rotate.
The disks complete the first full rotation at t = 1.7 seconds. What is the angular acceleration a of the disks?
a. 2.17 rad/s
b. 0.54 rad/s
c. 4.35 rad/s
How much work is done by the force applied to the rim of the larger disk between t = 0 and the time when the disks
have completed one full revolution? a. not enough information to tell
b. 13.7 J
c. 402.1 J
d. 51.2 J
e. 136 J
At the end of the first rotation, a force of constant magnitude is applied to the rim of the smaller disk, tangentially to
the rim, to counteract the force applied to the larger disk. What should the magnitude of the second force be for the
system of disks to maintain a constant angular velocity?
a. 106.7 N
b. 80 N
c. 60 N
Now the system of disks is brought back to rest and the smaller disk is removed. (Recall that both disks have mass
M
and their radii are and .) The same force F is applied to the rim of the remaining disk as before. How does the
angular acceleration of the larger disk alone, , relate to the angular acceleration of the system of two disks,
,measured previously? a. b. c. d. e. The next four questions pertain to the situation described below.
A beam has mass and length and can rotate without friction around a fixed axis which is perpendicular to
the x-y plane and which passes through the beam a distance to the left of its center as shown. Two forces
having the same magnitude act on the beam. The force acting at the right end is perpendicular to the beam,
and the force acting at the center makes an angle relative to the beam as shown. The moment of inertia of the
beam around the rotation axis shown is There is no gravity in this problem.
What is the mass of the beam ?
a. b. c. d. e. At the instant shown, in what direction is the center of the beam accelerating ?
a. In the -y direction.
b. In the +x direction.
c. In the +y direction.
At the instant shown, what is the magnitude of the angular acceleration of the beam around the rotation axis?
a. b. c. d. e. If the angle was increased to so that the force acting at the center was perpendicular to the beam, how would the
magnitude of the angular acceleration of the beam at the instant shown be different than in the above problem ?
a. It would be smaller.
b. It would be bigger.
c. It would stay the same.
The next four questions pertain to the situation described below.
A block (which you should treat like a point particle) has mass m = 0.31 kg
and slides with initial speed . It hits and sticks a distance D = 1.8 from the
end of a horizontal rod of length L = 2.4 m and mass M = 0.47 kg, which is
initially at rest and oriented perpendicular to the path of the block. Everything
is on top of a horizontal frictionless table, and the rod has a fixed frictionless
pivot through its end that allows it to rotate freely but keeps its end from
moving. After the block hits the rod they rotate together with a constant angular velocity of = 5.5 rad/sec. What was the initial
speed of the block?
a. = 18.79 m/s
b. = 9.9 m/s
c. = 8.89 m/s
d. = 2.22 m/s
e. = 12.12 m/s
As the block rides on the rod, it eventually slides further to the edge of the rod ultimately sticking at the very edge, a
distance L from the pivot. What is the speed of the block as it rotates around with the rod at this new location?
a. 7.02 m/s
b. 9.36 m/s
c. 13.2 m/s
Compare the kinetic energy of system (block+rod) when the mass is a distance D from the end, to the kinetic energy of
the system when it is at a distance L from the end.
a. KE
< KE
b. KE
> KE
c. KE
= KE
What is the direction of the angular momentum of the rod as it spins around the pivot?
a. into the page
b. out of the page
The next three questions pertain to the situation described below.
A gyroscope made from a solid disk of mass M = 6.6 kg and radius R = 0.41 m hangs from a
rope attached to the ceiling. The disk spins around a horizontal axle through its center in the
direction shown by the arrow, and the rope is attached to one end of this axle at a distance D =
1.42 m from the disk. The angular momentum of the disk is L = 89.6 kg-m
/s.
What is the magnitude of the angular velocity of the spinning disk?
a. = 194 rad/s
b. = 162 rad/s
c. = 242 rad/s
What direction will the Gyroscope precess from its current position?
a. out of the page (with the pivot on the string fixed, the gyroscope will come closer to you.)
b. into the page (with the pivot on the string fixed, the gyroscope will move further from you.)
What is the period of the precession of the gyroscope (in other words, the time needed to make one complete revolution
in the horizontal plane) ?
a. = 0.97 s
b. = 6.12 s
c. = 1.03 s
The next four questions pertain to the situation described below.
Suppose the moment of inertia of a ball about an axis through its center is given by the expression The ball
has mass and radius and rolls without slipping on a horizontal surface with an initial angular
velocity of What is the total kinetic energy of the ball as it rolls on the horizontal surface ?
a. b. c. d. e. What fraction of the total kinetic energy of the ball is due to rotation ?
a. b. c. Now suppose the ball rolls up an inclined plane and then rolls back down again. The angle of the incline with respect to
horizontal is and the ball does not slip on the incline. As the ball rolls down the ramp, what is the magnitude
of its acceleration?
a. b. c. d. e. When the ball is at its highest point on the ramp, which of the following statements best describes the direction of its
angular acceleration ?
a. points into the page.
b. points out of the page.
c. is zero.
The next two questions pertain to the situation described below.
A ladder of length = 6 meters and mass = 17 kg leans on a wall at an
angle of = 46 degrees. The coefficient of static friction between the floor
and the ladder is . There is no friction between the ladder and the wall.
A man of mass = 60 kg climbs a distance d up the ladder.
Which diagram best represents the free body diagram of the ladder?
a. Diagram (i)
b. Diagram (ii)
c. Diagram (iii)
What is the minimum value of the coefficient of static friction that would allow the man to climb to the top of the
ladder?
a. 0.86
b. 0.62
c. 0.38
d. 0.35
e. 0.75
The next four questions pertain to the situation described below.
A beam of mass m and length L is hinged and extends outward perpendicular to a wall, as
shown. A string is attached to the end of the beam with its other end attached to the wall a
distance L/3 above the hinge; the tension in that string is T = 80 N. A mass M = 1.8 kg hangs a
distance L/4 from the end of the beam.
What is the mass, m, of the beam?
a. 2.5 kg
b. 12.8 kg
c. Cannot be determined unless a value for L is provided
d. 0.7 kg
e. 4.5 kg
What is the x-component of the force exerted by the hinge on the beam?
a. 53.3 N
b. 25.3 N
c. Cannot be determined unless a value for L is provided
d. 75.9 N
e. 40 N
Suppose that the string is now attached higher at a distance of L/2 above the hinge and the tension adjusts (it is no
longer 80 N) so that the set-up remains in equilibrium. How would the x-component of the force exerted by the hinge
on the beam change from previously?
a. It would increase
b. It would remain the same
c. It would decrease
Now suppose that the string is cut from the original situation at the top of the page. In terms of m, M, g and L, which
expression below is gives the magnitude of the angular acceleration of the beam about the hinge immediately after the
string is cut?
a. b. c. Copyright © 2024 Department of Physics
, University of Illinois at Urbana-Champaign | Privacy Statement
two disks
D
L
D
L
D
L
2
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Unit 25: Homework / Homework / Homework / Homework / Homework /
Physics 211 Fall 2023
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