Question 8.1: BATTLE OF THE REVOLVING DOOR GOAL Apply the basic definition...
BATTLE OF THE REVOLVING DOOR
GOAL Apply the basic definition of torque.
PROBLEM Two disgruntled businesspeople are trying to use a revolving door, which is initially at rest (see Fig. 8.3.) The woman on the left exerts a force of 625 \mathrm{~N} perpendicular to the door and 1.20 \mathrm{~m} from the hub’s center, while the man on the right exerts a force of 8.50 \times 10^{2} \mathrm{~N} perpendicular to the door and 0.800 \mathrm{~m} from the hub’s center. Find the net torque on the revolving door.
STRATEGY Calculate the individual torques on the door using the definition of torque, Equation 8.1,
\tau = rF [8.1]
and then sum to find the net torque on the door. The woman exerts a negative torque, the man a positive torque. Their positions of application also differ.
Calculate the torque exerted by the woman. A negative sign must be supplied because \overrightarrow{\mathbf{F}}_{1}, if unopposed, would cause a clockwise rotation:
\tau_{1}=-r_{1} F_{1}=-(1.20 \mathrm{~m})(625 \mathrm{~N})=-7.50 \times 10^{2} \mathrm{~N} \cdot \mathrm{m}
Calculate the torque exerted by the man. The torque is positive because \overrightarrow{\mathbf{F}}_{2}, if unopposed, would cause a counterclockwise rotation:
\tau_{2}=r_{2} F_{2}=(0.800 \mathrm{~m})\left(8.50 \times 10^{2} \mathrm{~N}\right)=6.80 \times 10^{2} \mathrm{~N} \cdot \mathrm{m}
Sum the torques to find the net torque on the door:
\tau_{\text {net }}=\tau_{1}+\tau_{2}= – 7.0 \times 10^{1} \mathrm{~N} \cdot \mathrm{m}
REMARKS The negative result here means that the net torque will produce a clockwise rotation.