living with the lab Moments and Torque also

living with the lab Moments and 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. d 1 d 2 F 1 F 2

living with the lab Definition of a Moment d F A UNITS: 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. 2

living with the lab Consider the moment of F about point A for the cases below. line of action F ctio A n d of a A F line d lin e o line f a A on cti d A ctio n F F of a 3

living with the lab Class Example 1 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. 8 in 1 ft A b. n 6 i F 2 = 80 lbs F 1 = 100 lbs 4

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

living with the lab What is the difference between a moment and a torque? 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 6 N-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. 6

living with the lab 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 q = 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 q = 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 q = 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 q when both people are riding. e. Using Mathcad, plot the net moment for q = 0° to q = 360°. f. Assumptions: g. Ignore dynamic effects. h. Assume the weights of Uncle Fred and Freddie are centered at the pin where their chairs are connected to the circular structure. 7