Answer to Question #143351 in Physics for Zech

Question

A 3.0 meters long solid shaft makes an angle of 35 degrees with the horizontal. A vertical force of 50 N is applied 0.60 m from the upper end. What is the magnitude of the torque due to the vertical force about each end?

Answer 1

How to calculate torque if the force is not perpendicular to the shaft?

Torque is the length of lever times perpendicular component of force. Also, the torque is positive when it 'tries' to rotate is counter-clockwise and it is negative when it tries to rotate a rod clockwise. With this in mind, draw the figure:

Torque due to the vertical force about the lower end:

$$\tau_1=-50\text{ cos}35°\cdot2.4=98\text{ Nm}.$$

About the higher end:

$$\tau_2=50\text{ cos}35°\cdot0.6=25\text{ Nm}.$$