1. Motion and Forces in 2 and 3 Dimensions Torque and Rotation

2. Chapter 9 Objectives  Calculate the torque created by a force.  Solve problems by balancing two torques in rotational equilibrium.  Define the center of mass of an object.  Describe a technique for finding the center of mass of an irregularly shaped object.  Calculate the moment of inertia for a mass rotating on the end of a rod.  Describe the relationship between torque, angular acceleration, and rotational inertia.

3. Chapter 9 Vocabulary Terms  torque  center of mass  angular acceleration  rotational inertia  rotation  translation  center of rotation  rotational equilibrium  lever arm  center of gravity  moment of inertia  line of action

4. Torque Key Question: How does force create rotation?

5. Torque  A torque is an action that causes objects to rotate.  Torque is not the same thing as force.  For rotational motion, the torque is what is most directly related to the motion, not the force.

6. Torque  Motion in which an entire object moves is called translation.  Motion in which an object spins is called rotation.  The point or line about which an object turns is its center of rotation.  An object can rotate and translate.

7. Torque  Torque is created when the line of action of a force does not pass through the center of rotation.  The line of action is an imaginary line that follows the direction of a force and passes though its point of application.

8. Torque  To get the maximum torque, the force should be applied in a direction that creates the greatest lever arm.  The lever arm is the perpendicular distance between the line of action of the force and the center of rotation

10. Torque  = r x F Lever arm length (m) Force (N) Torque (N. m) Clockwise rotation is a negative torque. Counter clockwise rotation is a positive torque

11. Calculate a torque  A force of 50 newtons is applied to a wrench that is 30 centimeters long.  Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm.

12. Rotational Equilibrium  When an object is in rotational equilibrium, the net torque applied to it is zero.  Rotational equilibrium is often used to determine unknown forces.  What are the forces (F A, F B ) holding the bridge up at either end?

13. Rotational Equilibrium

14. Calculate using equilibrium  A boy and his cat sit on a seesaw.  The cat has a mass of 4 kg and sits 2 m from the center of rotation.  If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?

15. When the force and lever arm are NOT perpendicular

16. Calculate a torque  It takes 50 newtons to loosen the bolt when the force is applied perpendicular to the wrench.  How much force would it take if the force was applied at a 30-degree angle from perpendicular?  A 20-centimeter wrench is used to loosen a bolt.  The force is applied 0.20 m from the bolt.

17. Center of Mass Key Question: How do objects balance?

18. Center of Mass  There are three different axes about which an object will naturally spin.  The point at which the three axes intersect is called the center of mass.

19. Finding the center of mass  If an object is irregularly shaped, the center of mass can be found by spinning the object and finding the intersection of the three spin axes.  There is not always material at an object’s center of mass.

21. Finding the center of gravity  The center of gravity of an irregularly shaped object can be found by suspending it from two or more points.  For very tall objects, such as skyscrapers, the acceleration due to gravity may be slightly different at points throughout the object.

22. Balance and center of mass  For an object to remain upright, its center of gravity must be above its area of support.  The area of support includes the entire region surrounded by the actual supports.  An object will topple over if its center of mass is not above its area of support.