Answer:
Suppose we have a 6-foot board with a 10-pound bag of flour on it. If we put a pivot under
the board, the flour will create a torque on the board. Torque is like force, but it tends to
rotate things instead of moving them in a straight line. The torque generated by the flour is
T = r × F
where F is the force that gravity exerts on the flour (i.e., 10 lb), and r is the distance from
the pivot to the bag. So if the pivot is in the middle of the board (x = 3 ft) and the flour is
a foot to the right (x = 4 ft) then the torque is
(4 ft − 3 ft) × 10 lb = 10 ft·lb.
The greater a torque is, the more the board will tend to rotate. This explains how a wrench
works: you put a long wrench on a stuck bolt and push, and you generate a torque which
is greater (because of the length of the wrench) than if you just tried to turn the bolt with
your hand.
The board above will tend to rotate clockwise. If, instead of the flour on the right, we put
a 10 pound block of ice to the left of the pivot at x = 2, like this:
2
10
0 6
then the board will tend to rotate counterclockwise. To keep the two cases straight, we’ll
say that the flour was generating a torque of +10 ft·lb and the ice is generating a torque of
−10 ft·lb. Positive torque means clockwise, negative means counterclockwise. We can keep
our simple formula “T = r × F” by making r negative when the weight is to the left of the
pivot and positive when it’s to the right. That’s what we get when we set
r = (x-position of weight) − (x-position of pivot).
Having signed torques is convenient, because if we have both the flour and ice on the board,
2
10
4
10
Explanation:
