Practice Problems
Torque, Pulleys, and Rotational Motion
Directions:
On this worksheet you will practice using the basic formulas for torque and the subsequent rotational behavior.
omit
Question 1
A pulley of radius R = 31 cm is created from a solid cylinder suspended on a frictionless axle. One end of a cord is wrapped around the pulley's edge while the other end is attached to a block having a mass of 289 grams. The system is initially at rest.
When the system is released, the mass falls 1.6 meters in 3.1 seconds. What was the linear acceleration of the mass?
5.6 x 10
^{-1}
m/sec
^{2}
3.33 x 10
^{-1}
m/sec
^{2}
5.71 x 10
^{-1}
m/sec
^{2}
9.8 x 10
^{-1}
m/sec
^{2}
omit
Question 2
What is the tension in the cord while the mass is accelerating?
9.82 N
2.83 N
2.93 N
2.74 N
omit
Question 3
What torque does the cord deliver to the pulley while the mass is decending?
0.848 mN
0.883 mN
0.878 mN
0.908 mN
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Question 4
What angular impulse does the cord deliver to the pulley during the 3.1 seconds that the mass is decending?
8.48 N sec
2.63 N sec
8.78 N sec
9.08 N sec
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Question 5
Based on the fact that the cord did not slip as the mass fell, what is the angular acceleration of the pulley?
9.31 x 10
^{-1}
rad/sec
^{2}
3.16 x 10
^{0}
rad/sec
^{2}
1.03 x 10
^{-1}
rad/sec
^{2}
1.07 x 10
^{0}
rad/sec
^{2}
omit
Question 6
Based on these kinematics of the falling block, what is the pulley's experimental moment of inertia?
0.911 kg m
^{2}
0.817 kg m
^{2}
0.943 kg m
^{2}
0.790 kg m
^{2}
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Question 7
How much potential energy did the block possess at the start of the experiment?
4.532 J
2.983 J
0 J, it is at rest
0.259 J
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Question 8
What was the translational kinetic energy of the block at 3.1 seconds?
0.453 J
4.378 J
0.154 J
0.925 J
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Question 9
What was the rotational kinetic energy of the pulley at 3.1 seconds?
8.151 J
4.207 J
4.378 J
2.629 J
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Question 10
How much angular momentum does the pulley have at 3.1 seconds?
2.63 x 10
^{0}
kg m
^{2}
/sec
2.98 x 10
^{-1}
kg m
^{2}
/sec
2.53 x 10
^{0}
kg m
^{2}
/sec
8.15 x 10
^{-1}
kg m
^{2}
/sec
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Question 11
Once the experiment was over, the pulley is placed on a scale and its mass is determinied to be 17 kg. Calculate its actual moment of inertia?
0.795 kg m
^{2}
0.636 kg m
^{2}
0.530 kg m
^{2}
1.591 kg m
^{2}
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Question 12
What was the percent error for the experimental moment of inertia calculated in
Question #3
?
0.993 %
0.713 %
0.183 %
0.718 %
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Question 13
Based on the data obtained and analyzed in this experiment, was mechanical energy conserved?
No. Energy must have been lost
based on the fact that the experimental
moment of inertia was slightly incorrect.
No. Energy cannot be conserved if
linear momentum is not conserved.
no since the cord provided
a continuous torque to the pulley
yes, PE = KE
_{trans}
+ KE
_{rot}
omit
Question 14
If the pulley had been a wheel resembling a bicycle with the majority of its mass located in its rim and tire, but supported by thin, light-mass, wire spokes, which of the following would you expect to be true?
the pulley's angular acceleration
would decrease since its
moment of inertia increased
both the pulley's angular
acceleration and its moment
of inertia decrease
both the pulley's angular
acceleration and its moment
of inertia increase
the pulley's angular acceleration
would increase since its
moment of inertia decreased
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