1. Chapter 8.1 and 8.2 Torque and Angular Rotation

2. Definition of Torque Torque is the quantity that measures the ability of a force to rotate an object around some axis (fulcrum). ◦ Units – Nm Lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. Torque depends on Force and the length of the lever arm. Torque = Force x lever arm τ = Fr

3. Torque (cont.) ◦ Only the perpendicular component of the force produces a torque. ◦ The lever arm is the distance between the point where the force is applied and the axis of rotation (known as the fulcrum). ◦ By convention, we treat counterclockwise torque as positive, clockwise as negative. ◦ Torque like displacement and force is a vector quantity

4. Sample problem 1 Find the torque produced by a 3 N force applied to a door at a perpendicular distance of 0.25 m from the hinge. ◦ Known?  F = 3N, d = 0.25m ◦ Unknown?  τ = ? ◦ Equation?  τ = Fd  τ = 3 (.25) = 0.75 Nm

5. Torque problem 2 In the picture below, the person on the left weighs 900 N, and the person on the right weighs 400 N. If the person on the right is sitting 3 m from the fulcrum and the seesaw is balanced, how far must the person on the left be from the fulcrum? ◦ Known: Equation: Fr = Fr ◦ Unknown:

6. Chapter 8.3 Center of Mass

8. The Center of Mass SECTION 8.3 Equilibrium

9. The center of mass of a person varies with posture. For a person standing with his or her arms hanging straight down, the center of mass is a few centimeters below the navel, midway between the front and back of the person’s body. The Center of Mass of a Human Body SECTION 8.3 Equilibrium

10. When the arms are raised, as in ballet, the center of mass rises by 6 to10 cm. SECTION 8.3 Equilibrium The Center of Mass of a Human Body

11. By raising her arms and legs while in the air, as shown below, a ballet dancer moves her center of mass closer to her head. SECTION 8.3 Equilibrium The Center of Mass of a Human Body

12. The path of the center of mass is a parabola, so the dancer’s head stays at almost the same height for a surprisingly long time. SECTION 8.3 Equilibrium The Center of Mass of a Human Body

13. Center of Mass and Stability Click image to view movie. SECTION 8.3 Equilibrium