7.3 Torque (7.3)

Torque Overview

  • Torque Definition: The rotational equivalent of force; measures the effectiveness of a force in causing an object to rotate about a pivot.

  • Components Influencing Torque:

    • Magnitude of force ($F$)

    • Distance from pivot/axis ($r$)

    • Angle of force application ($\phi$)

Torque Formula

  • Basic Formula: \tau = r F_{\perp}

    • Where $F_{\perp}$ is the component of the force acting perpendicular to the radial line.

  • Alternate Expressions:

    • \tau = r F \sin(\phi)

    • \tau = r_{\perp} F

  • SI Unit: Newton meter (N·m)

Torque Direction and Sign

  • Positive Torque: Counterclockwise rotation.

  • Negative Torque: Clockwise rotation.

  • Zero Torque: Occurs when the force direction is either pushing straight toward or pulling straight away from the pivot.

Net Torque

  • Net Torque Calculation: \tau{\text{net}} = \tau{1} + \tau{2} + \tau{3} + …

    • Each torque can be summed algebraically, considering direction.

Practical Applications

  • When applying a force, increasing distance from the pivot or the angle of application can increase torque.

  • Example Problem: Calculating torque on a stuck door with given distances and angles.

  • Effective torque can be optimized by pushing perpendicularly to maximize $F_{\perp}$.

Conclusion

  • Understanding torque is essential for solving problems related to rotational motion and forces. Each factor—magnitude, distance, and angle—plays a crucial role in determining the resulting torque about a pivot point.

Certainly! One practical example mentioned in the notes is determining the torque required to open a stuck door. To calculate this, you would use the formula \tau = r F \sin(\phi).

Imagine the door's hinges as the pivot point. The distance $r$ would be measured from the hinges to where you apply the force on the door handle. The force $F$ is the magnitude of the push or pull you exert. The angle $\phi$ is between the radial line (from the hinges to the handle) and the direction of your applied force. To maximize the effectiveness of your effort (i.e., generate the most torque), the notes suggest pushing perpendicularly to the door, which means $\phi = 90^{\circ}$, making $\sin(\phi) = 1$. If the door is stuck, you might need to apply a greater force or apply it further from the hinges to achieve the necessary net torque to overcome the resistance.