0.14 Phy1110: force -- moments, torque, couple, and equilibrium  (Page 4/13)

By definition, (see College Physics by Mendenhall, Keys, Eve, and Sutton)

The torque or moment of a force about an axis through the point O is defined as theproduct of the force and the perpendicular distance from O to the line of action of the force.

Do torque and moment of a force mean the same thing?

This definition would have you believe that the torque of a force and the moment of a force mean the same thing. If you Google the difference betweentorque and moment, you will find many who agree that they mean the same thing and many who disagree. However, for practical purposes in this module, we willassume that they mean the same thing.

The turning action has a direction

Like force, the turning action of torque has a direction. Unlike force, however, for which the direction is a line through a point, the direction of the turning action of a torque is rotationalabout a point. The direction can be either clockwise or counter-clockwise. In this module, we will assume that a counter-clockwise direction is positive and aclockwise direction is negative.

(Although the turning action of a torque is rotational about a point, the true direction of a torque is said to be perpendicular to the plane containingthe forces. That topic is beyond the scope of this module.)

A machine that converts force to torque

A crank is a machine that converts force along a line into torque about a point. When the crank arm on my automobile jack is horizontal with the crank handle to the right, andI push down on the crank handle, a clockwise torque is developed about the axle at the other end of the crank arm.

That axle is actually a large screw, and the torque causes the screw to turn. The other end of that screw is threaded througha mechanism that is often referred to as a "scissors jack." The rotational motion of the screw causes a small platform to raise underneath my car to liftit off the ground.

Oops, need to change direction

When I push down on the crank handle and the screw begins to turn, the crank arm rotates along with the screw. Therefore, the crank arm is no longerhorizontal but is oriented at an angle slightly south of east. In order to keep the screw turning, I must adjust the direction of my force to being a littlewest of south instead of being straight down. As the process continues, I must continually adjust the direction of the force to be perpendicular to the lengthof the crank arm.

Discussion and sample code

Let's begin the discussion by expanding the conditions for equilibrium beyond the conditions that we have considered in earlier modules.

Conditions for equilibrium

In order for a body to be in equilibrium,

The vector sum of all forces acting on the body must be zero and the sum of all torques acting on the body measuredabout any axis must be zero.

Equilibrium for a body with an arbitrary shape

Achieving equilibrium may be easier said than done for a body with an arbitrary shape. Let's consider what first appears to be asimple example. Using your graph board, mark out a square that is four units on each side. You should probably make it rather large using four or five divisionson the graph board to represent one unit. Let this square represent a square board that is free to move horizontally or vertically and is also free torotate.