2. Causing Rotational Motion In order to make an object start rotating about an axis, a force is required However, not only the amount of force applied but also the position from the axis to which it is applied is important in determining the amount of rotation (angular acceleration Distance from axis is called the Lever Arm

3. Torque Definition Combination of amount of force and distance from axis is called Torque (τ) A torque is necessary in order to provide angular acceleration τ = rF r- dist from axis Units - N m In order to use this equation, the force must be perpendicular to the axis of rotation

4. Example 1 A biceps muscle exerts a vertical force on the lower arm as shown. Calculate the torque acting on the lower arm if the muscle is attached 5.0 cm from the elbow.

5. Example 2 A wrench is pulled by a force of 30 N at an angle of 30° with the axis and a distance of 15cm from its pivot end. What torque is acting on it?

6. Equilibrium Occurs when total force acting balance and no rotational motion occurs In order for equilibrium to exist, the total torque acting in the clockwise direction must balance the total torque acting in the counterclockwise direction

7. See-Saw When stationary, the total τ clockwise is equal to the τ counterclockwise If kid A pushes up with more force, the τ is no longer balanced (more force clockwise) and the see-saw begins to rotate clockwise with an angular velocity

9. Example 3 Two people are sitting on a seesaw that is 2.5 m long. One has a mass of 40 kg and the other a mass of 60 kg. Where would the support on the see-saw need to be placed in order to produce equilibrium?

10. Example 4 A 7.0 m beam is hanging from the ceiling by two ropes on its ends. The bar has a mass of 300 kg and it is non-uniform, with its center of mass 3.0 m from one end. A 400kg mass is hung from the beam’s light end and a 200 kg mass is hung from its heavy end. What force is acting on each rope?