CP Workbook
Torque: Cams and Spools
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Part I.
Felix Flex pulls the bar forward, rotates the cam, and lifts the load. Two torques act on the cam:
the counter-clockwise torque produced by Felix's pull
P
,
and the clockwise torque produced by the tension
T
that supports the load.
Note that although
T
stays constant, the torque is not constant because of the variable lever arm (hence the cam's odd shape!).
Shown below is the cam in three positions, A, B, and C. The lever arm (heavy dashed line) is shown for position A. Discuss with your partner the locations of the different-length lever arms for positions B and C. Sketch them on your papers. Notice that the cam provides a changing lever arm! Take care that your lever arm is perpendicular to the line of action of
T
.
Type the word "done" to view the correct answers. The first blank is for B, the second one is for C.
In which position does the cam provide the longest lever arm?
A
B
C
In which position does
T
produce the greatest torque?
A
B
C
In which position does the cam provide the shortest lever arm?
A
B
C
In which position does
T
produce the least torque?
A
B
C
Which position requires the least pull
P
for Felix to rotate?
A
B
C
Which position requires the most pull
P
for Felix to rotate?
A
B
C
Part II
Pull the string gently and the spool rolls. The direction of roll depends on the way the torque is applied.
There are two spools of sewing string/thread in the cabinet next to my teacher station if you want to "see" what happens. This also works with a yo-yo if someone wants to bring one to class on Friday.
In (1) and (2) below, the force and lever arm are shown for the torque about the point where surface contact is made (shown by the triangular "fulcrum"). The lever arm is the heavy dashed line, which is different for each different pulling position.
Discuss with your partner the locations of the different-length lever arms for the other positions. Sketch them on your papers.
Type the word "done" to view the correct answers. The first blank is for 3, the second one is for 4.
Type the word "done" to view the correct answers for 5-8.
The lever arm is longer when the string is on the ____ of the spool spindle.
top
bottom
For a given pull, the torque is greater when the string is on the
top
bottom
For the same pull, rotational acceleration is greater when the string is on
At which positions does the spool roll to the left?
At which positions does the spool roll to the right?
At which position does the spool not roll at all?
Why does the spool slide rather than roll at this position?
Part III
We all know that a ball rolls down an incline. But relatively few people know that the reason the ball picks up rotational speed is because of a torque.
In Sketch A, we see the ingredients of the torque acting on the ball - the force due to gravity and the lever arm to the point where surface contact is made. Construct the lever arms for positions B and C.
Type the word "done" to view the correct answers for B and C.
As the incline becomes steeper, the torque
increases
decreases
remains the same
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Rotational Kinematics #2
Paul G. Hewitt
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All rights reserved.
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