1. Moments and Torque living with the lab Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist. d1d1 F1F1 F2F2 d2d2

2. living with the lab 2 Definition of a Moment The moment or torque of the force F about point A is a measure of the tendency of F to produce rotation about point A. F d A UNITS:

3. living with the lab 3 Consider the moment of F about point A for the cases below. d A F line of action d F A d F A F A

4. living with the lab 4 Class Example F 1 = 100 lbs A 1 ft 1 in 6 in 8 in The semicircular segment pivots about point A. a.What is the moment of F 1 about A? b.What is the moment of F 2 about A? a. F 2 = 80 lbs b.

5. living with the lab 5 Class Example F = 100N 55° Find the moment of F about point A. d 1 = 2m d 2 = 3m A +

6. What is the difference between a moment and a torque? living with the lab 6 The words moment and torque are often used interchangeably. A moment and a torque are physically the same thing; they are both a measure of the tendency of a force or set of forces to produce rotation. Moment is a more general term than torque. A torque is a special application of a moment and generally refers to the tendency to produce rotation about an axle. Typical usage of these words can vary by discipline and location. A gearmotor can output a peak torque of 6N-m (physical rotation occurs about the motor shaft). The weight of a child who climbs out on the branch of a tree will induce a moment on the limb; the moment will be maximum at the base of the branch.

7. living with the lab 7 Class Problem Uncle Fred who weighs 200 lbs. is riding a Ferris wheel at the county fair along with his 80 lb. son, Freddie. The Ferris wheel has a diameter of 30 feet. a.What moment will Uncle Fred exert about the center of rotation (point A) when  = 45° if he is the only one riding? Will this moment act clockwise (CW) or counter clockwise (CCW)? b.What moment will Freddie exert about the center of rotation (point A) when  = 45° if he is the only one riding (his angle is actually 45° + 90° = 135°)? Will this moment act CW or CCW? c.What is the net moment about point A when  = 45° and both are riding? Assume that a CW moment is positive and a CCW moment is negative. Is the net moment CW or CCW? d.Derive an equation for the moment about point A as a function of  when both people are riding. e.Using Mathcad, plot the net moment for  = 0° to  = 360°. Assumptions: Ignore dynamic effects. Assume the weights of Uncle Fred and Freddie are centered at the pin where their chairs are connected to the circular structure.