1. Torque

2. Tough Nut  Which of the four arrangements is best for tightening a bolt? ABCD

3. Pivot Point  Rotation of a wheel or wrench takes place with an axis of rotation.  The point where the axis intersects the object is the pivot point.  r  pivot point

4. Lever Arm  The tangential force acts at a distance away from the pivot point.  The distance from the pivot to the force is called the lever arm, or moment arm. r lever arm points out from the pivot

5. Perpendicular Component  Only the perpendicular component of the force can affect the tangential acceleration.  For an angle (  ) between the force (F) and lever arm (r), the perpendicular component is Fsin .  angle between lever arm and force

6. Moment of Force  The force exerted on the lever arm is the moment of force.  This is called torque (  ).

7. Changing a Tire  A wheel nut needs 95 N-m of torque.  A 45 cm wrench makes a 67° angle with the horizontal.  The horizontal force needed: r  °  °

8. Torque Wrench  Consider the product rFsin . rF(0.7)2rF = (1.4)rF (0.87)rF(3r/2)(F/2) = (3/4)rF

9. Torque and Work  A force does work on an object acting over a distance.  A torque does work on an object rotating through an angle. r 

10. Conservation of Energy  The net work done by forces on an object equals the change in kinetic energy.  The net work done by torques on an object equals the change in rotational kinetic energy.

11. Rotational Power  As with translational motion, power is the rate of work done.  The earth is slowing due to the tides. About 28 s / century 1 part in 10 8  The kinetic energy is changing.  The power dissipation is large: About 7 billion hp next