1. Torque

2. Torque Torque results when a force acts to rotate an object Torque results when a force acts to rotate an object A force applied to some point other than the center of gravity A force applied to some point other than the center of gravity To C of G  Translational To C of G  Translational To off C of G  Rotational To off C of G  Rotational Leverage – torque produced when force applied with leverage Leverage – torque produced when force applied with leverage Ex. Doorknob far away from turning axis (hinges) Ex. Doorknob far away from turning axis (hinges) Direction of Force is perpendicular to plane Direction of Force is perpendicular to plane

3. Torque Torque dependent on: Torque dependent on: 1. Distance from turning axis 1. Distance from turning axis Lever arm Lever arm Distance from point of contact to axis Distance from point of contact to axis 2. Perpendicular component of applied force 2. Perpendicular component of applied force τ = F d τ = F d τ = Torque; F = perpendicular force; d = distance from center τ = Torque; F = perpendicular force; d = distance from center

4. Torque Three wrenches – same force applied. Which would do the best job? Three wrenches – same force applied. Which would do the best job? 1 2 3

5. See-saw Balance if torques equal. Balance if torques equal. What if not equal? What if not equal?

8. Meter Stick Example 20 cm90 cm 50 cm 20 N? N Counterclockwise Torque = Clockwise Torque  Balance AB F ┴A x D A = F ┴B x D B

9. Coupled Forces Two forces of equal magnitude but opposite direction in the same plane but not the same point Two forces of equal magnitude but opposite direction in the same plane but not the same point Pair of forces such as this is coupled: Pair of forces such as this is coupled: The torque equals the product of one of the forces and the perpendicular distance between The torque equals the product of one of the forces and the perpendicular distance between Can’t be balanced with a single force, must balance with another couple Can’t be balanced with a single force, must balance with another couple F F xAxA xBxB

10. Review Torque Torque Produces a clockwise or counterclockwise motion when a force is applied at a point other than the center of gravity Produces a clockwise or counterclockwise motion when a force is applied at a point other than the center of gravity τ = F d τ = F d Three Conditions Three Conditions F left = F right F left = F right F up = F down F up = F down F clockwise = F counterclockwise F clockwise = F counterclockwise The arrows tell you if the force is clockwise or counterclockwise The arrows tell you if the force is clockwise or counterclockwise

11. Example Problem 100 lbs 20 lbs 40 lbs 2 ft 3 ftx F clockwise = F counterclockwise