1. Rotational Dynamics and Static Equilibrium
Chapter 11
Rotational Dynamics and Static Equilibrium

2. Outline Torque Torque for a tangential force
General definition of torque
Sign convention for torque

3. Torque in everyday life

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

7. 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. 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. 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. 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 F1 = 72 N and F2 = 58 N. Find
(a) the torque caused by F1
(b) the torque caused by F2
(c) In which direction does the wheel turn as a result of these two forces?