1. Rotational Equilibrium and Rotational Dynamics Rotational Motion 1 of 25 Physics 2053 Lecture Notes

2. Rotational Equilibrium and Dynamics 9-01 Torque 8-02 Torque and the Conditions for Equilibrium 8-03 Center of Gravity 8-04 Examples of Objects in Equilibrium Dynamics: Newton’s Laws of Motion Topics

3. Torque F r The force used to open a door produces a torque Static Equilibrium Torque

4. Two equal forces are applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque? A) the first at the midpoint B) both exert equal non-zero torques C) both exert zero torques D) the second at the doorknob Rotational Equilibrium

5. Torque R r F  Static Equilibrium Torque

6. Two equal forces are applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30° to the plane of the door. Which force exerts the greater torque? A) the first applied perpendicular to the door B) the second applied at an angle C) both exert equal non-zero torques D) both exert zero torques Rotational Equilibrium

7. Conditions for Equilibrium  F = 0   = 0 Static Equilibrium Torque and the Conditions for Equilibrium

8. x 3 = 20 cm 3 kg2 kg o N = ? x 2 = ? 2nd Condition of Equilibrium 1st Condition of Equilibrium A massless meter stick What is the Normal Force What is the Distance x 2 Static Equilibrium Torque and the Conditions for Equilibrium

9. cg x cm x1x1 x2x2 x y m1m1 m2m2 Linear Momentum Center of Gravity

10. Find the center of gravity of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass. Problem 0.5 m 0.25 m 1.0 kg 1.5 kg 1.1 kg x y Linear Momentum

11. Center of Gravity L Find x cg L = 150 cm W = 600 N W b = 50 N F = 200 N

12. Linear Momentum Center of Gravity L L = 150 cm W = 600 N W b = 50 N F = 200 N F N

13. WBWB WTWT N1N1 N2N2 1 st Condition 2 st Condition Truck on a Bridge Static Equilibrium Examples of Objects in Equilibrium

14. WBWB WTWT N1N1 N2N2 1 st Condition 2 nd Condition Truck on a Bridge Static Equilibrium Examples of Objects in Equilibrium

15. Hanging a Sign Physics WBWB WSWS T N F  Static Equilibrium Examples of Objects in Equilibrium

16. d L  T WBWB WSWS  d = L sin(  ) Hanging a Sign 1 st Condition N F 2 nd Condition Find Tension in cable Static Equilibrium Examples of Objects in Equilibrium

17. WBWB T N F  d L How far (d) can a student walk on beam before cable breaks (T max ) WSWS Static Equilibrium Examples of Objects in Equilibrium

18. When T reaches T max WBWB T max N F  d L WSWS o Walking Student Static Equilibrium Examples of Objects in Equilibrium