1. Torque http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html DO NOW: Serway Read Pages 306 – 308 Do Example 10.10 page 309 Define and Utilize : Moment arm – Lever Arm Line of Action Net torque CCWτ= positive CWτ= negative Equilibrium Homework: Serway 10.6 page 320 #’s 32 – 34 all http://ia600508.us.archive.org/2/items/AP_Ph ysics_C_Lesson_16/Container.html

2. Torque A torque is an influence which tends to change the rotational motion of an object. Torque = (Force applied )(lever arm) lever arm The lever arm is defined as the perpendicular distance from the axis of rotation to the line of action of the force.

3. Lever Arm

4. Torque Calculation θ

5. Torque Equilibrium Examples Most equilibrium problems require the application of force as well as torque for their solution, but the examples below illustrate equilibrium of torque.equilibriumforce

6. http://hyperphysics.phy- astr.gsu.edu/hbase/mstk.html Torque Equilibrium Example For an extended system to be at equilibrium,equilibrium The sum of the torques must be equal to zero.torques Assuming that the beam is supported under its center of mass, it will contribute no torque.center of mass The torque equation in terms of the weights is thenweights

7. Support of a Boom The support of a pivoted, uniform boom with a cable is a standard exercise in equilibrium of torques.equilibriumtorques Using a pivot at the wall, which is assumed to exert no torque, the torque equation is that shown below. The forces exerted on the boom are then obtainable from the force equation shown. All Torques in the CW direction = ZERO All Torques in the CCW direction = ZERO The lever arm for the cable tension T must be obtained from the triangle as shown since the cable is not perpendicular to the boom. http://hyperphysics.phy- astr.gsu.edu/hbase/boom.html

8. Supporting an Extended Load For an extended system to be at equilibrium,equilibrium The sum of the forces must be equal to zeroforces and the sum of torques about any axis must equal zero.torques Choose one of the ends as the axis since that eliminates one of the unknown forces (lever arm = zero).lever arm Considering a long uniform wooden board, note that the mass of the board can be considered to be concentrated at its center of mass for the purposes of calculating torque. For a uniform board, the center of mass is at its geometrical center, so the lever arm with respect to either end of the board will be L/2.center of mass Choosing the left end as the axis, the torque and force equilibrium equations are shown below. http://hyperphysics.phy- astr.gsu.edu/hbase/extms.html

9. Quick Lab: Center of Mass and Torque PURPOSE: This demonstration illustrates the following concepts: (1)balance of torques, (2)friction and the normal force, (3)finding the center of gravity. DESCRIPTION: Balance the meter stick on your two index fingers, with one finger initially at one end and the other finger about one-quarter of the way from the other end. Slide your fingers together (moving either one or the other or both). What Will Happen? SUGGESTIONS: Try different starting points. Try adding a 100 gram weight onto either end. Try greasing your finger. What Will Happen? Your fingers will always end up together directly under the center of mass.