1. Torque ► Consider force required to open door. Is it easier to open the door by pushing/pulling away from hinge or close to hinge? close to hinge away from hinge Farther from from hinge, larger rotational effect! Physics concept: torque

2. Torque ►T►T►T►Torque,, is the tendency of a force to rotate an object about some axis  i s the torque dddd i i i is the lever arm (or moment arm) FFFF i i i is the force Door example:

3. Direction of Torque ►T►T►T►Torque is a vector quantity TTTThe direction is perpendicular to the plane determined by the lever arm and the force DDDDirection and sign: IIIIf the turning tendency of the force is counterclockwise, the torque will be positive IIIIf the turning tendency is clockwise, the torque will be negative Direction of torque: out of pageUnitsSI Newton meter (Nm) US Customary Foot pound (ft lb)

4. ConcepTest 2 You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is most effective in loosening the nut? List in order of descending efficiency the following arrangements:

5. ConcepTest 2 You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is most effective in loosening the nut? List in order of descending efficiency the following arrangements: 2, 1, 4, 3 or 2, 4, 1, 3

6. What if two or more different forces act on lever arm?

7. Net Torque ► The net torque is the sum of all the torques produced by all the forces  Remember to account for the direction of the tendency for rotation ► Counterclockwise torques are positive ► Clockwise torques are negative

8. Example 1: Given: weights: w 1 = 500 N w 2 = 800 N lever arms: d 1 =4 m d 2 =2 m Find:  = ? 1. Draw all applicable forces 2. Consider CCW rotation to be positive 500 N 800 N 4 m2 m Rotation would be CCW N Determine the net torque:

9. Where would the 500 N person have to be relative to fulcrum for zero torque?

10. Example 2: Given: weights: w 1 = 500 N w 2 = 800 N lever arms: d 1 =4 m  = 0 Find: d 2 = ? 1. Draw all applicable forces and moment arms 500 N 800 N 2 md 2 m According to our understanding of torque there would be no rotation and no motion! N’ y What does it say about acceleration and force? Thus, according to Newton’s 2 nd law  F=0 and a=0!

11. Example of a Free Body Diagram ► Isolate the object to be analyzed ► Draw the free body diagram for that object  Include all the external forces acting on the object