1. Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 11 Rotational Dynamics and Static Equilibrium

2. Dr. Jie Zou PHY 1151G Department of Physics2 Outline Torque Torque for a tangential force General definition of torque Sign convention for torque

3. Dr. Jie Zou PHY 1151G Department of Physics3 Torque in everyday life

4. Dr. Jie Zou PHY 1151G Department of Physics4 Definition of torque, , for a tangential force Tangential force: An applied force that is tangential to a circle of radius r centered on the axis of rotation. For a tangential force,  = rF SI units: N  m F: magnitude of the force r: distance from the axis of rotation to the force

5. Dr. Jie Zou PHY 1151G Department of Physics5 Example To open the door in the figure a tangential force F is applied at a distance r from the axis of rotation. If the minimum torque required to open the door is 3.1 N·m, what force must be applied if r is (a) 0.94 m, or (b) 0.35 m?

6. Dr. Jie Zou PHY 1151G Department of Physics6 Radial and tangential components of force A radial force produces zero torque. Only tangential component produces torque.

7. Dr. Jie Zou PHY 1151G Department of Physics7 General definition of torque,  In general,  = r(F sin  )  : the angle of the force relative to the radial direction. Two special cases: (1) For a radial force,  =0, and  =r(F sin 0)=0; (2) For a tangential force,  =  /2, and  =r(F sin  /2)=rF.

8. Dr. Jie Zou PHY 1151G Department of Physics8 The moment arm, r  The moment arm, r  : The perpendicular distance from the axis of rotation to the line of the force is defined to be r . r  = r sin  SI unit: m Torque is the moment arm times the force:  = r(F sin  ) = (r sin  )F = r  F

9. Dr. Jie Zou PHY 1151G Department of Physics9 Sign convention for torque Sign convention for torque: If a torque  acts alone, then  >0 if the torque causes a counterclockwise angular acceleration.  <0 if the torque causes a clockwise angular acceleration. In a system of more than one torque, the sign of each torque is determined by the type of angular acceleration it alone would produce. The net torque acting on the system is the sum of each individual torque, taking into account the proper sign.

10. Dr. Jie Zou PHY 1151G Department of Physics10 Example Two helmsmen exert the forces shown below on a ship’s wheel. The wheel has a radius of 0.74 m, and the two forces have the magnitudes F 1 = 72 N and F 2 = 58 N. Find (a) the torque caused by F 1 (b) the torque caused by F 2 (c) In which direction does the wheel turn as a result of these two forces?

11. Dr. Jie Zou PHY 1151G Department of Physics11 Homework See online homework assignment on www.masteringphysics.com www.masteringphysics.com